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Michael Joseph Halm
hierogamous@lycos.com
<http://untilheaven.tripod.com/id112.html>Sequences</a>
Sequences
  Some of the sequences referenced in the club's other pages are further explained here. Some are officially recognized by the On-line Encyclopedia of Integer Sequences, OEIS. Many are new.
*aban: [e:a::eban:?] referring to integers without a -- 0, 1, 2, 3, ..., 999, 1000000, 1000001,  ..., 1000999, 2000000, 2000001, ...
abelian  A051532 referring to interger both cube-free with prime divisors satisfying certain congruences.-- 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 113, 115
*Abntu: [Bantu alphome] A072809 alphadigital Bantu -- 10, 11, 13, 41, 51, 16, 17, 81, 91, 30, 13, 33, 43, 53, 63, 73, 83, 93, 40, 41,  43, 44, 54, 46, 47, 84, 49, 50, 51, 53, 54, 55, 56, 57, 85, 59, 60, 16, 63, 46,  56, 66, 67, 68, 69, 70, 17, 73, 47, 57, 76, 77, 87, 97, 80, 81, 83, 84, 85, 86,  87, 88, 89, 90, 91, 93, 49, 59, 96
abundant: A005101 referring to integer n whose sum of its factors > 2n -- 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270
*acci: [nonacci backformation] integer not nonacci, f(n) = N(f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) + f(n - 5) + f(n - 6) + f(n - 7) + f(n - 8) + f(n - 9)) -- 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 129
*agonal: [nonagonal backformation] integer not nonagonal  f(n) = N(n(7n - 5)/2)-- 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70
almost-natural: A007376 f(n) = d(max(i)), where n = sum(G(2, i, 10)d(i)) -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 4, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 5, 0,
*almost-perfect: 2, 1, 0, 1, 8, 2, 2, 9, 9, 0, 1, 2, 3, 4, 2, 4, 7, 9, 3, 1, 6,  0, 0, 3, 6, 2, 2, 8, 5, 0, 5, 6, 0, 8, 6, 8, 9, 6, 1, 8, 4, 8, 2, 7, 2, 2, 3, 7, 2, 6, 3, 6, 0, 3, 3, 2, 8
*alphadigital: A072763 referring to integer with digits in alphabetical order --10, 11, 12, 13, 41, 51, 16, 17, 81, 91, 20, 12, 22, 32, 42, 52, 62, 72, 82, 92,  30, 13, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 46, 47, 84, 49,  50, 51, 52, 53, 54, 55, 56, 57, 85, 59, 60, 16, 62, 63, 46, 56, 66, 67, 68, 69,  70, 17, 72, 73, 47, 57, 76, 77, 87
amicable: A063990 referring to integers whose divisors add to each other, sum(div(n)) = sum(div(n + 1)) -- 220, 284; 1184, 1210; 2620, 2924; 5020, 5564; 6232, 6368; 10744, 10856; 12285, 14595; 17296, 18416; 63020, 66928; 66992, 67095; 69615, 71145; 76084, 79750; 87633, 88730; 100485, 122265; 122368, 123152; 124155, 139815; 141664, 142310
Apery A005259 f(n + 1) = ((G(2, 3, 34n) + G(2, 2, 51n) + 27n + 5)f(n) - G(2, 3, n)f(n - 1))/G(2, 3, n + 1), n = 1 -- 1, 5, 73, 1445, 33001, 819005, 21460825, 584307365, 16367912425, 468690849005, 13657436403073, 403676083788125, 12073365010564729, 364713572395983725
Aronson: A005224 referring to integer generated by the sentence, “T is the first, fourth, eleventh, ... letter in this sentence.”: 1, 4, 11, 16, 24, 29, 33, 35, 39, 45, 4 7, 51, 56, 58, 62, 64, 69, 73, 78, 80, 84, 89, 94, 99, 104, 111, 116, 122, 126, 131, 136, 142, 147, 158, 164, 169, 174, 181, 183, 193, 199, 205, 208, 214, 220, 226, 231, 237, 243, 249, 254, 270, 288, 303, 307, 319, 323, 341
autobiographical: [Walt Bates, Aug. 1987 Puzzle-M] referring to integers which tally own digits left-to-right from zero -- 1210, 21200, 3211000, 42101000, 521001000, 6210001000, 72100001000, 821000001000, 9210000001000
balanced: A020492 referring to integers whose count of integers less than or equal to n and prime to n divides the sum of its divisors 1, 2, 3, 6, 12, 14, 15, 30, 35, 42, 56, 70, 78, 105, 140, 168, 190, 210, 248, 264, 270, 357, 418, 420, 570, 594, 616, 630, 714, 744, 812, 840, 910, 1045, 1240, 1254, 1485, 1672, 1848, 2090, 2214, 2376, 2436, 2580, 2730, 2970, 3080, 3135, 3339, 3596, 3720, 3828
*Bantu: A052404 referring to integer without 2 -- 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 30, 31, 33, 34, 35,  36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57,  58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79,  80, 81, 83, 84, 85, 86, 87, 88, 89
Bell: aka  exponential, A000110 referring to ways of placing n labeled balls into n indistinguishable boxes -- 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323
Benford: A004002 referring to integers, f(n) = [G(2, 2, e, e) + 1/2] -- 1, 3, 15, 3814279
betrothed: A005276 aka quasi-amicable, referring to integers, sum((div(n)) = sum(div(n(i)))) ± 1, where div(n) = divisor of n -- 48, 75; 140, 195; 1050, 1575; 1648, 1925; 2024, 2295; 5775, 6128; 8892, 9504; 16587, 20735; 62744, 75495; 186615, 196664; 199760, 206504; 219975, 266000; 309135, 312620
binary-sieved: referring to integers left after successively deleting every G(2, n, 2)th integer -- 1, 3, 5, 9, 11, 13, 17, 21, 25, 27, 29, 33, 35, 37, 43, 49, 51, 53, 57, 59, 65, 67, 69, 73, 75, 77, 81, 85, 89, 91, 97, 101, 107, 109, 113, 115, 117, 121, 123, 129, 131, 133, 137, 139, 145, 149
*biographical: referring to integer which tallies one or more other integers' digits left-to-right from zero -- 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, ..., 9999999999
*bicomposite: [prime:biprime::composite:?] referring to composite with at least four prime factors which may or may not be different, f(n) = Np(i)Np(j) -- 16, 18, 20, 24, 28, 30, 32, 36, 40, 48, 50, 54, 56, 60, 64, 72, 80, 81, 84, 88, 90, 96, 100, 104, 108, 112,  120, 126, 128, 132, 135, 136, 140, 144, 150, 152, 156, 160, 162, 168, 176, 180, 184, 189, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 225, 228, 232, 234, 240, 243, 248, 250, 252, 256, 260, 264, 268, 270, 272, 276, 280, 282, 286, 288, 290, 294, 297, 298, 300
biprime: A001358 referring to composite with only two prime factors, f(n) = p(i)p(j) -- 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141,  142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187
cake: A000125 referring to maximal integer of pieces resulting from n planar cuts through a cube (or cake)  -- 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, 9178, 9920, 10701, 11522, 12384, 13288, 14235, 15226
*Caliban: A072958 referring to integer without a, c, i or l -- 1, 2, 3, 4, 7, 10, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70,  71, 72, 73, 74, 77, 100, 101, 102, 103, 104, 107, 110, 114, 117, 120, 121, 122, 123, 124, 127, 140, 141, 142, 143, 144, 147, 170, 171, 172, 173, 174,  177, 200, 201, 202, 203, 204, 207
Carmichael:  A002997 referring to composite integers n such that G(2, n -1, a) = 1 (mod n) if a is prime to n -- 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461
Catalan:  A000108 aka Segnar, referring to integer f(n) = (2n)!/(n!(n + 1)!) -- 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324
*CATS: [cube-add-then-sort] f(n) = sort(G(2, 3, n) + n) -- 1, 3, 68, 13, 222, 35, 25, 378, 11, 1234, 147, 122, 2578, 339, 1124, 349, 558, 6788, 28, 2289, 167, 1129, 13488, 1556, 1267,1179, 1289, 12448, 237, 22289. 238, 3579, 33389, 1249, 24669, 569, 1459, 35589, 446, 26689, 1347, 5579, 22588, 1179, 23789, 1378, 1146, 116789, 1255, 12237
*ceefpart: [perfect alphome with phonetic r] alphadigitally perfect -- 6, 82, 496, 8812, 5563333, 888559966, 884911763332, 8885549911333222, 5555555444449999911117766666633222
*cheap: referring to integers with 1, 2 or 3, but not two -- 1, 2, 3, 11, 22, 33, 111, 222, 333, 1111, 2222, 3333, 11111, 22222, 33333, 111111, 222222, 333333, 1111111, 2222222, 3333333, 11111111, 22222222, 33333333
*cheaper: : referring to integers with any two of 1, 2 or 3 -- 12, 13, 21, 23, 31, 32, 112, 113, 121, 122, 131, 133, 211, 212, 221, 223, 232, 233, 311, 313, 322, 323, 1112, 1113, 1121, 1122, 1211, 1212,
*cheapest: : referring to integers with 1, 2 and 3 only -- 123, 132, 213, 231, 312, 321, 1123, 1132, 1213, 1231, 1312, 1321, 2123, 2132, 2213, 2231, 2312, 2321, 3123, 3132, 3213, 3231, 3312, 3321, 11123, 11132, 11213, 11231, 11312, 11321, 12123, 12132, 12213, 12231, 12312, 12321
Collatz: A006577 -- referring to number of halving and tripling steps to reach 1 in `3x + 1' problem -- 0, 1, 7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, 7, 7, 15, 15, 10,  23, 10, 111, 18, 18, 18, 106, 5, 26, 13, 13, 21, 21, 21, 34, 8, 109, 8, 29, 16,  16, 16, 104, 11, 24, 24, 24, 11, 11, 112, 112, 19, 32, 19, 32, 19, 19, 107,  107, 6, 27, 27, 27, 14, 14, 14, 102, 22
composite: A002808 referring to non-prime integers, f(n) = Np = G(1, G(2, i, p(j)), G(2, k, p(m)) -- 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88
congruent: A003273 referring to positive integers n for which there exists a right triangle having area n and rational sides, n = ij/2 -- 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 30, 31, 34, 37, 38, 39, 41, 45, 46, 47, 52, 53, 54, 55, 56, 60, 61, 62, 63, 65, 69, 70, 71, 77, 78, 79, 80, 84, 85, 86, 87, 88, 92, 93, 94, 95, 96, 101, 102, 103, 109, 110, 111, 112, 116, 117, 118, 119, 120, 124, 125, 126
Connell: A001614 referring to integers taken in alternately odd and even groups, f(n) = 2n - [(1 + G(2, 1/2, ((8n - 7))/2)] -- 1, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 37, 39, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 122
Cuban: [A. J. C. Cunningham] A002407 referring to integer for which (G(2, 3, (x + 1) - G(2, 3, x)) = p -- 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227
cube: A000578 f(n) = G(2, 3, n) -- 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653
*cubefull: [square:squarefull::cube:?] referring to integer divisible by a prime cubed, f(n) = 0 (mod G(2, 3, p)) -- 8, 16, 27, 32, 64, 81, 125, 128, 243, 256, 343, 375, 500, 512, 686, 729, 750, 889, 1000, 1024, 1029, 1125, 1250, 1331, 1372, 1375, 1458, 1500, 1625, 1715, 1750, 1900, 2025, 2048, 2058, 2150, 2187, 2197
Cullen: A002064 referring to integers, f(n) = nG(2, n, 2) + 1 -- 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521, 44040193, 92274689, 192937985, 402653185, 838860801, 1744830465, 3623878657, 7516192769
curious: A003226 aka automorphic, referring to integers for which G(2, 2, n) = n (mod 10) 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 8212890625, 18212890625, 81787109376, 918212890625, 9918212890625, 40081787109376, 59918212890625
*curvaceous: A072960 referring to integer written with curves only, i. e., with 0, 3, 6, 8 or 9 -- 0, 3, 6, 8, 9, 30, 33, 36, 38, 39, 60, 63, 66, 68, 69, 80, 83, 86, 88, 89, 90,  93, 96, 98, 99, 300, 303, 306, 308, 309, 330, 333, 336, 338, 339, 360, 363,  366, 368, 369, 380, 383, 386, 388, 389, 390, 393, 396, 398, 399, 600, 603,  606, 608, 609, 630, 633, 636, 638, 639
*curvilinear: A072961 referring to integer which is both curved and linear,  i. e., 2 or 5 -- 2, 5, 22, 25, 52, 55, 222, 225, 252, 255, 522, 525, 552, 555, 2222, 2225,  2252, 2255, 2522, 2525, 2552, 2555, 5222, 5225, 5252, 5255, 5522, 5525,  5552, 5555, 22222, 22225, 22252, 22255, 22522, 22525, 22552, 22555, 25222, 25225, 25252, 25255
*dear: referring to integers with 7, 8, or 9 but not two -- 7, 8, 9, 77, 88, 99, 777, 888, 999, 7777, 8888, 9999, 77777, 88888, 99999, 777777, 8888888, 999999, 7777777, 8888888, 9999999, 77777777, 88888888, 99999999
*dearer: referring to integers with any two of 7, 8, or 9 -- 78, 79, 87, 97, 98, 778, 787, 788, 877, 878, 887, 977, 979, 997, 7778, 7779, 7787, 7788, 7797, 7799, 7877, 7878, 7977, 7979, 8777, 8778, 8787, 8788,
*decacci: Fibonacci-like sequence but adding previous 10, f(n) = f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) + f(n - 5) + f(n - 6) + f(n - 7) + f(n - 8) + f(n - 9) + f(n - 10) -- 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172, 16336, 32656, 65280, 130496, 260864, 521472, 1042432, 2083841, 4165637, 8327186, 16646200, 33276064, 66519472, 132973664
decagonal: A001107 f(n) = 4G(2, 2, n) - 3n -- 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267
deficient: A005100 referring to integers for which sum(div(n)) < 2n - 1, where div(n) = divisor of n -- 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77
Demlo: A002477 referring to integers, f(n) = G(2, 2, ((G(2, n + 1, 10) -1)/9)) -- 1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 1234567900987654321, 123456790120987654321, 12345679012320987654321, 1234567901234320987654321
*DENEAT: A073053 referring to integer generated by application of DENEAT (digits-even-not-even-and-total) operator -- 11, 101, 11, 101, 11, 101, 11, 101, 11, 22, 112, 22, 112, 22, 112, 22, 112,  22, 112, 202, 112, 202, 112, 202, 112, 202, 112, 202, 112, 22, 112, 22,  112, 22, 112, 22, 112, 22, 112, 202, 112, 202, 112, 202, 112, 202, 112,  202, 112, 22, 112, 22, 112, 22, 112, 22
*deneaticity: A073054 referring to  number of applications of DENEAT (digits-even-not-even-and-total) operator needed to reduce n to 123.-- 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,  4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3,  2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,  4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 1, 2, 1, 2, 1
denumerant: A000115 referring to integers,  [G(2, 2, n + 4)/20 + ½] -- 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 18, 20, 22, 24, 26, 29, 31, 34, 36, 39, 42, 45, 48, 51, 54, 58, 61, 65, 68, 72, 76, 80, 84, 88, 92, 97, 101, 106, 110, 115, 120, 125, 130, 135, 140, 146, 151, 157, 162, 168, 174, 180, 186, 192, 198
*deutero-Collatz: A072761 referring to modified Collatz sequence allowing change of x to 3x+1 even when x = 2n -- 0, 1, 7, 2, 5, 8, 8, 3, 11, 5, 9, 9, 8, 9, 9, 4, 9, 12, 14, 7, 7, 11, 12, 10
*digital power: [addition:exponentiation::digital sum:?] A075877  f(n) = G(2, d(i), ...(G(2, d(2), G(2, d(2), d(1)) where n = sum(G(2, i, 10)d(i)) -- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 3, 9, 27,
*digital product: [addition::multiplication::digital sum:?] A007954 prod(d(i)), where n = sum(G(2, i, 10)d(i))   -- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3,
digital reversal: A004086 -- f(n) = sum(G(2, i, 10)(d(max(i) - i + 1)), where n = sum(G(2, i,10)d(i)) -- 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 6
digital root A010888 -- f(n) = sum(...(sum(d(sum(d(i )))))...), where n =  sum(G(2, i, 10)d(i)) -- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9
digital sum A007953 -- prod(d(i)), where n = sum(G(2, i, 10)d(i))  -- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
dodecahedral: A006566 referring to integers, n(3n - 1)(3n - 2)/2. -- 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, 14190, 17296, 20825, 24804, 29260, 34220, 39711, 45760, 52394, 59640, 67525, 76076, 85320, 95284, 105995, 117480, 129766, 142880, 156849, 171700, 187460, 204156
double factorial: A006882 n!!: f(n) = nf(n - 2) -- 1, 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 81749606400, 316234143225, 1961990553600, 7905853580625, 51011754393600
*double primorial: [factorial:primorial::double factorial:?] A07907 n## = p(i)p(i - 2)##; ((2n)## = product(p(2i)) and  (2n + 1)## = product(p(2i + 1)), where p(n) = nth prime -- 2, 3, 10, 21, 110, 273, 1870, 5187, 43010, 150423, 1333310, 5565651, 54665710, 239322993, 2569288370, 12684118629, 151588013830, 773731236369, 8640516788310, 54934917782199, 630757725546630, 4339858504793720
Dowling: A003581 referring to integers, G(2, k + (G(2, 9k - 1, e)/9, e) -- 1, 2, 13, 143, 1852, 27563, 473725, 9290396, 203745235, 4912490375, 128777672338, 3643086083981, 110557605978901, 3579776914324250, 123074955978249433, 4474133111905169219, 171363047274358839412
Duffinian: A003624 referring to integers n, composite and relatively prime to sum(divs(n)) -- 4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, 64, 65, 75, 77, 81, 85, 93, 98, 100, 111, 115, 119, 121, 125, 128, 129, 133, 143, 144, 155, 161, 169, 171, 175, 183, 185, 187, 189, 201, 203, 205, 209, 215, 217, 219, 221, 225, 235, 237, 242, 243, 245, 247
eban: A006933 referring to integers without e -- 2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, 2000, 2002, 2004, 2006, 2030, 2032, 2034, 2036, 2040, 2042, 2044, 2046, 2050, 2052, 2054, 2056, 2060, 2062, 2064, 2066, 4000, 4002, 4004, 4006, 4030, 4032, 4034, 4036, 4040, 4042, 4044, 4046, 4050, 4052, 4054, 4056, 4060, 4062, 4064, 4066, 6000, 6002, 6004, 6006, 6030, 6032, 6034, 6036, 6040, 6042, 6044, 6046, 6050, 6052, 6054, 6056, 6060, 6062, 6064, 6066, 30002
economical: A046759 referring to integers,  f(n) = sum(G(2, i, p(j)))  with D(n) = number of digits in product, d(n) = number of digits in n;  sequence gives n such that D(n) < d(n)  -- 125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875, 2048, 2187, 2197, 2209, 2401, 2560, 2809, 3125, 3481, 3584, 3645, 3721, 4096, 4374, 4375, 4489, 4802, 4913
emirp:[prime ananym] non-palindromic prime whose reversal is also prime -- 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193
energetic: A055480 referring to integers f(n) = G(2, x, k) + G(2, y, m) = x(G(2, z, 10) + y -- 24, 43, 63, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 132, 135, 142, 153, 175, 209, 224, 226, 262, 264, 267, 283, 284, 332, 333, 334, 357, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 407, 445, 463, 518, 568, 598, 629, 739, 794, 809, 849, 935, 994, 1000
Euclid: A006862 referring to integers for which f(n) = 1 + sum(p(i)) -- 2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, 6469693231, 200560490131, 7420738134811, 304250263527211, 13082761331670031, 614889782588491411, 32589158477190044731, 1922760350154212639071
Euler: A000364 or up/down integers: expansion of sec x  +  tan x . Also alternating permutations on n letters -- 1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521, 353792, 2702765, 22368256, 199360981, 1903757312, 19391512145, 209865342976, 2404879675441, 29088885112832, 370371188237525, 4951498053124096, 69348874393137901
even: A005843 referring to integer 2n -- 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120
evenly-even: 4n -- 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88
evil: A001969 referring to integer with even number of ones  (base 2) -- 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 63, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 95, 96, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 129
factorial: A000142 referring to integers with n consecutive integers as factors, n! = prod(i) -- 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000
factorial differences-and-sums primes: 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, 1226280710981, 19696509177019, 335990918918981
Fermat: G(2, 2, n, 2) + 1. (It is conjectured that just the first 5 integers in this sequence are primes.) 5, 17, 257, 65537, 4294967297, 18446744073709551616
fibbinary: [Marc LeBrun] A003714 referring to intergers for which if n = F(i(1)) + F(i(2)) + ... + F(i(j)) is the Zeckendorf representation of n (i.e. in Fibonacci integer system) then f(n) = G(2, i(1) -2, 2) + G(2, i(2) - 2, 2) + ... + G(2, i(j) - 2, 2) -- 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457,   115792089237316195423570985008687907853269984665640564039457584007913129639937,     13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084097
Fibonacci: A000045 referring to integers F(n) = F(n - 1) + F(n - 2), F(0) = 0, F(1) = 1, F(2) = 1, F(n) = G(2, n, (1 + G(2, 1/2, 5))) - (1 - G(2, n, G(2, 1/2, 5))/(G(2, n., 2)G(2, 1/2, 5) -- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169
Fibonacci-even: A022342 with even Zeckendorf expansion, sum(G(2, j, (F(i))) = 0 (mod 2) -- 0, 2, 3, 5, 7, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 41, 42, 44, 45, 47, 49, 50, 52, 54, 55, 57, 58, 60, 62, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 79, 81, 83, 84, 86, 87, 89, 91, 92, 94, 96, 97, 99, 100, 102, 104, 105, 107
*flawless: A073417 referring to integer without a,  f,  l or w -- 1, 3, 6, 7, 8, 9, 10, 13, 16, 17, 18, 19, 30, 31, 33, 36, 37, 38, 39, 61, 63, 66,  67, 68, 69, 70, 71, 73, 76, 77, 78, 79, 80, 81, 83, 86, 87, 88, 89, 90, 91, 93,  96, 97, 98, 99, 100, 101, 103, 101, 103, 106, 107, 108, 109, 110, 113, 116,  117, 118, 119, 130, 131, 133
flimsy:[K. B. Stolarsky] A005360 referring to integers whose multiples have anomalous digital frequencies -- 11, 13, 19, 22, 23, 25, 26, 27, 29, 38, 39, 41, 43, 44, 46, 47, 50, 52, 53, 54, 55, 57, 58, 59, 61, 71, 76, 77, 78, 79, 82, 86, 87, 88, 91, 92, 94, 95, 99, 100, 103, 104, 106, 107
fortunate: A005235 referring to integers where letting q(n) represent the least prime > x(n) = 1 + sum(p(i)), giving f(n) = q(n) - x(n) + 1 -- 3, 5, 7, 13, 23, 17, 19, 23, 37, 61, 67, 61, 71, 47, 107, 59, 61, 109, 89, 103, 79, 151, 197, 101, 103, 233, 223, 127, 223, 191, 163, 229, 643, 239, 157, 167, 439, 239, 199, 191, 199, 383, 233, 751, 313, 773, 607, 313, 383, 293, 443, 331, 283, 277, 271, 401, 307, 331
*four-is: A072425 referring to the sequence counting the number of letters in the words of the generating sentence, "Four is the number of letters in the first word of this sentence, two in the second, three in the third, six in the fourth, two in the fifth ..." -- 4, 2, 3, 6, 2, 3, 7, 2, 3, 5, 4, 24, 8, 3, 2, 3, 6, 5, 2, 3, 5, 3, 2, 3, 6, 3, 2, 3, 5,  5, 2, 3, 5, 5, 2, 3, 7, 3, 2, 3, 6, 5, 2, 3, 5, 4, 2, 3, 5, 4, 2, 3, 8, 3, 2, 3, 7, 5, 2,  3, 10, 5, 2, 3, 10, 2, 3, 9, 5, 2, 3, 9, 3, 2, 3, 11, 4, 2, 3, 10, 3, 2, 3, 10
Franel: A000172 referring to integers, G(2, 2, n + 1)f( n + 1) = (7G(2, 2, n) + 7n + 2)f(n) + 8G(2, 2, n)f(n - 1) -- 1, 2, 10, 56, 346, 2252, 15184, 104960, 739162, 5280932, 38165260, 278415920, 2046924400, 15148345760, 112738423360, 843126957056, 6332299624282, 47737325577620, 361077477684436, 2739270870994736, 20836827035351596
golden Beatty: [nf] -- 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 101
good: A000696 f(n) = s(1) - ms(2) where s(1) and s(2) are in S = {n = 0 w/o 2 or 3 (base 4)} 1, 7, 31, 37, 109, 121, 127, 133, 151, 157, 403, 421, 511, 529, 631, 637, 661, 679, 1579, 1621, 1633, 1969, 1981, 2017, 2041, 2047, 2053, 2071, 2077, 2143, 2149, 2167
grasshopper: A007319 referring to integer in the closed sequence: closed under the transformations of n into 2n + 2 and 6n + 6 -- 1, 4, 10, 12, 22, 26, 30, 46, 54, 62, 66, 78, 94, 110, 126, 134, 138, 158, 162, 186, 190, 222, 254, 270, 278, 282, 318, 326, 330, 374, 378, 382, 402, 446, 474, 510, 542, 558, 566, 570, 638, 654, 662, 666, 750, 758, 762, 766, 806, 810, 834, 894, 950, 954, 978
greengrocer: A002412 referring to hexagonal pyramidal integers, f(n) = n(n + 1)(4n - 1)/6 -- 0, 1, 7, 22, 50, 95, 161, 252, 372, 525, 715, 946, 1222, 1547, 1925, 2360, 2856, 3417, 4047, 4750, 5530, 6391, 7337, 8372, 9500, 10725, 12051, 13482, 15022, 16675, 18445, 20336, 22352, 24497, 26775, 29190, 31746, 34447, 37297, 40300
*great: referring to integers of form G(2, n = 2, A12A13A14,100) -- 1728, 2197, 2744, 20736, 28561, 38416, 248832, 371293, 537824, 2985984, 4826809, 7529536, 35831808, 62748517, 105413504, 429981696, 815730721,
1475789056, 5159780352, 10604499373, 20661046784, 61917364224, 137858491849, 289254654976, 743008370688, 1792160394037, 4049565169664, 8916100448256, 23298085122481, 56693912375296,
106993205379072, 302875106592253, 793714773254144, 1283918464548860, 3937376385699290
*half-copper: referring to integer with 4 or 9 but not two -- 4. 9, 44, 99, 444, 999, 4444, 9999, 44444, 99999, 444444, 999999, 4444444, 9999999
*half-goose: referring to integer with 1 or 3 but not two -- 1, 3, 11, 33, 111, 333, 1111, 3333, 11111, 33333, 111111, 333333, 1111111, 3333333
*half-hatchet: referring to integer with 5 or 6 but not two -- 5, 6, 55, 66, 555, 666, 5555, 6666, 55555, 66666, 555555, 666666
*half-heinz: referring to integer with 5 or 7 but not two -- 5, 7, 55, 77, 555, 777, 5555, 7777, 55555, 77777, 555555,777777, 5555555, 7777777
*half-lok: referring to integer with 2 or 4 but not two -- 2, 4, 22, 44, 222, 444, 2222, 4444, 22222, 44444, 222222, 444444, 2222222, 7777777
*half-partition: referring to integer with 4 or 6 but not two -- 4, 6, 44, 66, 444, 666, 4444, 6666, 44444, 66666, 444444, 666666
*half-sam: referring to integer with 1 or 2 but not two -- 1, 2, 11, 22, 111, 222, 1111, 2222, 11111, 22222, 111111, 222222
*half-step: referring to integer with 3 or 9 but not two -- 3, 9, 33, 99, 333, 999, 3333, 9999, 33333, 99999, 333333, 999999
*half-square: [quarter:half::quarter-square:?] [G(2, 2, n)/2] -- 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, 128, 144, 162, 180, 200, 220, 242, 262, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 848, 722, 760, 800, 840, 882, 924, 968, 1012, 1058
happy: A007770 referring to integers which end up at 1 under a finite number of iterations of SOSOD (sum of squares of digits, f(n) = sum(G(2, 2, d(i))) -- 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320
*happy couple: referring to integers, n and n + 1 which are both happy -- 32, 129, 130, 192, 193, 262, 263, 301, 302, 319, 320, 367, 368, 391, 392, 565, 566, 622, 623, 637, 638.655, 656, 912, 913, 931, 932, 1029, 1030, 1092, 1093, 1114, 1115, 1121, 1122, 1151, 1152, 1184, 1185, 1211, 1212, 1221, 1222, 1257, 1258, 1274, 1275, 1299, 1300, 1332, 1335, 1447, 1448, 1474, 1475, 1511, 1512, 1527, 1528, 1574, 1575, 1581, 1582, 1724, 1725, 1744, 1745, 1754, 1755, 1771, 1772, 1784, 1785, 1814, 1815, 1851, 1874, 1875, 1880, 1881, 1882, 1902, 1903, 1929, 1930, 2062, 2063
harmonic: A001599 aka Ore integers whose mean of divisors is integral, sum(div(i)/i(max(div(n)))) = j -- 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190, 18600, 18620, 27846, 30240, 32760, 55860, 105664, 117800, 167400, 173600, 237510, 242060, 332640, 360360, 539400, 695520, 726180, 753480, 950976, 1089270, 1421280, 1539720
*harmless: A073416 referring to integer without a, h, m or r. -- 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 29, 50, 51, 52, 55, 56,  57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80,  81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 1000000000,  1000000001, 1000000002
hendecagonal A051682 referring to integer f(n) = n(9n - 7)/2 -- 0, 1, 11, 30, 58, 95, 141, 196, 260, 333, 415, 506, 606, 715, 833, 960, 1096, 1241, 1395, 1558, 1730, 1911, 2101, 2300, 2508, 2725, 2951, 3186, 3430, 3683, 3945, 4216, 4496, 4785, 5083, 5390, 5706, 6031, 6365, 6708, 7060, 7421, 7791, 8170
heptagonal: A000566 referring to integer f(n) = n(5n - 3)/2 -- 0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970, 1071, 1177, 1288, 1404, 1525, 1651, 1782, 1918, 2059, 2205, 2356, 2512, 2673, 2839, 3010, 3186, 3367, 3553, 3744, 3940, 4141, 4347, 4558, 4774, 4995, 5221, 5452, 5688
*heptal: referring to integers expressible in base 7, i. e., without 7, 8, or 9 -- 0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 66, 100, 101, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 115, 116, 120, 121,
heptanacci: A066178 referring to integers formed like Fibonacci numbers, but by adding previous 7, f(n + 1) = f(n) + ... + f(n - 6) -- 1, 2, 4, 8, 16, 32, 64, 127, 253, 504, 1004, 2000, 3984, 7936, 15808, 31489, 62725, 124946, 248888, 495776, 987568, 1967200, 3918592, 7805695, 15548665, 30972384, 61695880, 122895984, 244804400, 487641600
hex: A003215 referring to centered hexagonal integers, f(n) = 3n(n + 1) + 1 -- 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, 1141, 1261, 1387, 1519, 1657, 1801, 1951, 2107, 2269, 2437, 2611, 2791, 2977, 3169, 3367, 3571, 3781, 3997, 4219, 4447, 4681, 4921, 5167, 5419, 5677, 5941, 6211, 6487
hexagonal: A000384  referring to integers, f(n) = n(2n - 1) -- 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560
hexagon: referring to integers with f(n) = G(2, 2, n) + nG(2, 2, n - 1) digits arrangable in hexagon -- 10000000, 10000001, ..., 99999998, 99999999, 10000000000000000000000
hexal: A007092 referring to integers expressible in base 6, i.e., without 6, 7, 8 or 9 -- 0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 100, 101, 102, 103, 104, 105, 110, 111, 112, 113, 114, 115, 120, 121, 122, 123, 124, 125, 130
hexanacci: A001592 referring to integers formed like Fibonacci numbers, but by adding previous 6 such numbers, f(n + 1) = f(n) + f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) + f(n - 5) -- 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976, 1936, 3840, 7617, 15109, 29970, 59448, 117920, 233904, 463968, 920319, 1825529, 3621088, 7182728, 14247536, 28261168, 56058368, 111196417, 220567305, 437513522, 867844316
hyperfactorial: A002109  product(G(3, 2, n)!) -- 1, 4, 108, 27648, 86400000, 4031078400000, 3319766398771200000, 55696437941726556979200000, 21577941222941856209168026828800000, 215779412229418562091680268288000000000000000,        61564384586635053951550731889313964883968000000000000000
hyperperfect: referring to integers, n = m(sum(div(n)) - n - 1) + 1 for some m > 1 -- 21, 301, 325, 697, 1333, 1909, 2041, 2133, 3901, 10693, 16513, 19521, 24601, 26977, 51301, 96361, 130153, 159841, 163201, 176661, 214273, 250321, 275833, 296341, 306181, 389593, 486877, 495529, 542413, 808861, 1005421, 1005649, 1055833, 1063141, 1232053
*hyperprimorial: [factorial:hyperfactorial::primorial:?] prod(G(2, p(i), (p(i))) --  4, 108, 337500, 277945762500, 79301169838123237015000
*icca: [prime:emirp::acci:?] 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 65
*Iccanobif:[Fibonacci ananym, see Iccanobif primes A036797] 0, 1, 1, 2, 3, 5, 8, 12, 31, 43, 55, 98, 332, 441, 773, 789, 1814,4852, 5676, 7951, 11771,52057, 64901, 75682, 86364, 118713, 393121, 814691, 922415  
icosahedral: A006564 referring to integer, n(G(2, 2, 5n) -5n + 2)/2 -- 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, 6384, 7890, 9616, 11577, 13788, 16264, 19020, 22071, 25432, 29118, 33144, 37525, 42276, 47412, 52948, 58899
*immodest: referring to integers not modest, n = N[n/G(2, x, 10)] (mod (n - [n/G(2, x, 10)])-- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90
*imperfect: referring to integers not perfect, n = Nsum(div(n)) -- 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59
impractical: A007621  referring to even abundant numbers that are not practical -- 70, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 350, 354, 366, 372, 402, 426, 438, 444, 474, 490, 492, 498, 516, 534, 550, 564, 572, 582, 606, 618, 636, 642, 650, 654, 678, 708, 732, 738, 748, 762, 770, 774, 786, 804, 822, 834, 836, 846, 852, 876, 894, 906, 910, 940, 942, 948
*interddo: [prime:interemirp::odd:?] referring to average of two consecutive odd numbers which when reversed are still odd  -- 2, 4, 6, 8, 10, 12, 14, 16, 18, 25, 32, 34, 36, 38, 45, 52, 54, 56, 58, 65, 72, 74, 76, 78, 85, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146
*interemirp: [prime:interprime::emirp:?] referring to average of two consecutive emirps -- 15, 24, 34, 51, 72, 76, 88, 102, 110, 131, 153, 162, 173, 189, 255, 324, 342, 353, 374, 545, 705, 721, 736, 741, 747, 756, 765, 838, 922, 939, 947, 960, 969, 977, 987, 1000, 1015, 1026, 1032, 1047, 1065, 1080, 1094, 1100, 1106, 1130, 1152, 1167, 1187
*interfortunate: [prime:interprime::fortunate:?] 4, 6, 10, 18, 20, 18, 21, 30, 49, 64, 64, 66, 59, 77, 83, 60, 85, 99, 96, 91, 115, 174, 149, 102, 163, 223, 175, 175, 207, 177, 196, 436, 441, 198, 162, 303, 339, 219, 195, 195, 291, 308, 492, 532, 543, 690, 460, 348, 338, 368, 387, 307, 280, 274, 336, 354, 319
*interJacobsthal-Lucas: [prime:interprime::Jacobsthal-Lucas:?] 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 27, 36, 38, 45, 52, 55, 58, 65, 72, 74, 77, 85, 92, 94, 96, 100, 104, 106, 108, 111, 114, 116, 118, 121, 124, 126, 128, 131, 134, 136, 138, 141, 144, 146, 148, 151, 154, 156, 158, 161, 164, 166, 168, 171, 174, 176, 178, 181
*interpodd: [prime:interprime::podd:?] referring to average of consecutive  palindromic odd integers -- 2, 4, 6, 8, 10, 22, 44, 66, 88, 100, 106, 112, 117, 136, 146, 156, 166, 176, 186, 247, 308, 318, 328, 338, 348, 358, 368, 378, 388, 449, 510, 520, 530, 540, 550, 560, 570, 580, 656, 712, 722, 732, 742, 752, 762, 772, 782, 853
interprime: A024675 referring to average of two consecutive odd primes -- 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129, 134, 138, 144, 150, 154, 160, 165, 170, 176, 180, 186, 192, 195, 198, 205, 217, 225, 228, 231, 236, 240, 246, 254, 260, 266, 270, 274, 279, 282, 288, 300
Jacobsthal-Lucas: A014551 referring to integers, f(n) = G(2, n, 2) + G(2, n, -1) -- 2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911, 1073741825, 2147483647, 4294967297, 8589934591, 8589934591, 17179869185, 34359738367, 68719476737, 137438953471, 274877906945, 549755813887, 1099511627777, 2199023255551, 4398046511105, 8796093022207, 17592186044417, 35184372088831, 70368744177665, 140737488355327, 281474976710657, 562949953421311
Jordan-Pólya: A001013 referring to integers which are the products of two factorials, n!m! -- 1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 120, 128, 144, 192, 216, 240, 256, 288, 384, 432, 480, 512, 576, 720, 768, 864, 960, 1024, 1152, 1296, 1440, 1536, 1728, 1920, 2048, 2304, 2592, 2880, 3072, 3456, 3840, 4096, 4320, 4608, 5040, 5184, 5760
Kaprekar: A006886 referring to integer n such that n = x + y and G(2, 2, n) = x10z + y, for some z = 1,  x = 0 and 0 = y < G(2, z, 10), with n! = G(2, a, 10), f(1) = 1 -- 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 17344, 22222, 38962, 77778, 82656, 95121, 99999, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170
Kendall-Mann: A000140 referring to maximal inversions in permutation of n letters, Largest coefficient of (1)(x + 1)(G(2, 2, x) + x + 1) ... (G(2, n, x) + ... + x + 1) -- 1, 1, 2, 6, 22, 101, 573, 3836, 29228, 250749, 2409581, 25598186, 296643390, 3727542188, 50626553988, 738680521142, 11501573822788, 190418421447330, 3344822488498265, 62119523114983224, 1214967840930909302
Lah: A008297 referring to integers, (n - 1)n!/2 -- 1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600, 199584000, 2634508800, 37362124800, 566658892800, 9153720576000, 156920924160000, 2845499424768000, 54420176498688000, 1094805903679488000, 23112569077678080000
Langford: [C. Dudley Langford] referring to integers with n digits between digits n -- 0, 101, 2002, 31013, 20121, 12102, 23123, 312132, 23421314, 41312432,2302131, 1312032
left factorial: A003422 !n = sum(i!) = n(!(n -1)-(n - 1)(!(n - 2)) -- 0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114, 4037914, 43954714, 522956314, 6749977114, 93928268314, 1401602636314, 22324392524314, 378011820620314, 6780385526348314, 128425485935180314, 2561327494111820314, 53652269665821260314
*left primorial: A079096 #n = sum(prod(pi))-- 1, 3, 9, 39, 249, 2559, 5559, 516069, 10215759, 233308629, 6703001859, 207263491989, 7628001626799, 311878265154009, 13394639596824039, 628284422185315449, 33217442899375360179, 1955977793053587999249
Loeschian: A003136 referring to integers of form G(2, 2, x) + xy + G(2, 2, y); norms of vectors in A2 lattice -- 0, 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 49, 52, 57, 61, 63, 64, 67, 73, 75, 76, 79, 81, 84, 91, 93, 97, 100, 103, 108, 109, 111, 112, 117, 121, 124, 127, 129, 133, 139, 144, 147, 148, 151, 156, 157, 163, 169, 171, 172, 175, 181, 183, 189, 192
look-and-say A005150 referring to operation in which digits are counted out, e. g., 1 = one 1 = 11 -- 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, 11131221133112132113212221,
3113112221232112111312211312113211
Loxton-van der Poorten: A006288 referring to integers whose base 4 representation contains only 0, 1, 3 -- 0, 1, 3, 4, 5, 11, 12, 13, 15, 16, 17, 19, 20, 21, 43, 44, 45, 47, 48, 49, 51, 52, 53, 59, 60, 61, 63, 64, 65, 67, 68, 69, 75, 76, 77, 79, 80, 81, 83, 84, 85, 171, 172, 173, 175, 176, 177, 179, 180, 181, 187, 188, 189, 191, 192, 193, 195, 196, 197, 203, 204, 205, 207, 208, 209
Lucas: A000032 referring to integers, L(n) = G(2, n, 1 + G(2, 1/2, 5)/2) + G(2, n, 1 - G(2, 1/2, 5)/2) -- 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043
lucky: A000959 referring to integers formed by deleting every third odd integer, then every seventh, leaving 1 3 7 9 13 ...;  etc. -- 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303
Lychrel: A023108 integers which apparently never result in a palindrome with repeated applications of reverse-and-add function -- 196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978, 986, 1495, 1497, 1585, 1587, 1675, 1677, 1765, 1767, 1855, 1857, 1945, 1947, 1997, 2494, 2496, 2584, 2586, 2674, 2676, 2764, 2766, 2854, 2856, 2944, 2946, 2996, 3493, 3495, 3583, 3585, 3673, 3675
manille: referring to integer with 2 or 7 -- 2, 7, 22, 27, 72, 77, 222, 227,  272, 277, 722, 727, 772, 777, 2222, 2227,  2272, 2277, 2722, 2727, 2772, 2777, 7222, 7227,  7272, 7277, 7722, 7727, 7772, 7777  
Maris-McGwire: A045759
 referring to integers for which f(n) = f(n + 1), where f(n) = sum of digits of n + sum of digits of prime factors of n (including multiplicities) -- 7, 14, 43, 50, 61, 63, 67, 80, 84, 118, 122, 134, 137, 163, 196, 212, 213, 224, 241, 273, 274, 277, 279, 283, 351, 352, 373, 375, 390, 398, 421, 457, 462, 474, 475, 489, 495, 510, 516, 523, 526, 537, 547, 555, 558, 577, 584, 590, 592, 616, 638, 644, 660, 673, 687, 691
Markoff: A002559 referring to union of integers x, y, z satisfying G(2, 2, x) + G(2, 2, y) + G(2, 2, z) = 3xyz -- 1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, 1597, 2897, 4181, 5741, 6466, 7561, 9077, 10946, 14701, 28657, 33461, 37666, 43261, 51641, 62210, 75025, 96557, 135137, 195025, 196418, 294685, 426389, 499393, 514229, 646018
meander: A005315 referring to closed meandric integers, ways a loop can cross a road 2n times -- 1, 1, 2, 8, 42, 262, 1828, 13820, 110954, 933458, 8152860, 73424650, 678390116, 6405031050, 61606881612, 602188541928, 5969806669034, 59923200729046, 608188709574124, 6234277838531806, 64477712119584604, 672265814872772972, 7060941974458061392
meandric: A005316 referring to ways a river can cross a road n times -- 1, 1, 1, 2, 3, 8, 14, 42, 81, 262, 538, 1828, 3926, 13820, 30694, 110954, 252939, 933458, 2172830, 8152860, 19304190, 73424650, 176343390, 678390116, 1649008456, 6405031050, 15730575554, 61606881612, 152663683494, 602188541928, 1503962954930, 5969806669034, 15012865733351, 59923200729046, 151622652413194, 608188709574124, 1547365078534578, 6234277838531806, 15939972379349178, 64477712119584604, 165597452660771610, 672265814872772972, 1733609081727968492, 7060941974458061392
ménage: A000179 referring to integers, f(n) = (1 + n)f(n - 1) + (2 + n)f(n - 2) + f(n - 3) -- 0, 3, 13, 83, 592, 4821, 43979, 444613, 4934720, 59661255, 780531033, 10987095719, 165586966816, 2660378564777, 45392022568023, 819716784789193, 15620010933562688, 313219935456042955, 6593238655510464741
Mersenne: A001348 referring to integer f(n) = G(2, p, 2) - 1 -- 3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 536870911, 2147483647, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 2305843009213693951
Mian-Chowla: A005282
*middling: referring to integer with only 4, 5 or 6 -- 4, 5, 6, 44, 55, 66, 444, 555, 666, 4444, 5555, 6666, 44444, 55555, 66666, 444444, 5555555, 6666666, 4444444, 5555555, 6666666
*middlinger: referring to integer with two of 4, 5 or 6 -- 45, 46, 54, 56, 64, 65, 445, 446, 454, 455, 464, 466, 544, 545, 554, 556, 565, 566, 644, 646, 655, 656, 664, 665,  4445, 4446, 4454, 4456, 4464, 4465
*middlingest: 456, 465, 546, 564, 645, 4654, 4456, 4465, 4546, 4564, 4645, 4654, 5456, 5465, 5546, 5564, 5645, 5654, 6456, 6465, 6546, 6564, 6645, 6654
minimal: A007416 referring to integers with smallest number of dividers arranged in increasing order -- 1, 2, 4, 6, 12, 16, 24, 36, 48, 60, 64, 120, 144, 180, 192, 240, 360, 576, 720, 840, 900, 960, 1024, 1260, 1296, 1680, 2520, 2880, 3072, 3600, 4096, 5040, 5184, 6300, 6480, 6720, 7560, 9216, 10080
(A005179 arranged by number of divisors: 1, 2, 4, 6, 16, 12, 64, 24, 36, 48, 1024, 60, 4096, 192, 144, 120, 65536, 180, 262144, 240, 576, 3072, 4194304, 360, 1296, 12288, 900, 960, 268435456, 720, 1073741824, 840, 9216, 196608, 5184, 1260, 68719476736, 786432, 36864, 1680, 1099511627776, 2880)
modest: A054986 referring to integer for which there exists at least one partitioning of its decimal expansion wherein the integer divided by the second part leaves a remainder of the first part, n = [n/G(2, x, 10)] (mod (n - [n/G(2, x, 10)]) -- 13, 19, 23, 26, 29, 39, 46, 49, 59, 69, 79, 89, 103, 109, 111, 133, 199, 203, 206, 209, 211, 218, 222, 233, 266, 299, 309, 311, 327, 333, 399, 406, 409, 411, 412, 418, 422, 433, 436, 444, 466, 499, 509, 511, 515, 533, 545, 555, 599, 609, 611, 618, 622, 627
Moran: A001101 referring to integers for which n/sum(d(i)) = p -- 18, 21, 27, 42, 45, 63, 84, 111, 114, 117, 133, 152, 153, 156, 171, 190, 195, 198, 201, 207, 209, 222, 228, 247, 261, 266, 285, 333, 370, 372, 399, 402, 407, 423, 444, 465, 481, 511, 516, 518, 531, 555, 558, 592, 603
Moser-de Bruijn: A000695 referring to integers  sum(G(2, i, 4)) -- 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, 85, 256, 257, 260, 261, 272, 273, 276, 277, 320, 321, 324, 325, 336, 337, 340, 341, 1024, 1025, 1028, 1029, 1040, 1041, 1044, 1045, 1088, 1089, 1092, 1093, 1104, 1105, 1108, 1109
Motzkin: A001006 referring to number of ways of drawing nonintersecting chords among n points on a circle, f(n) = (1/(n + 1))sum(n + 1)!/(i!(i + 1)!(n - 2i)!) -- 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 25669818476, 73007772802, 208023278209, 593742784829
MU-integer: A007335 referring to integers multiplicatively uniquely the product of 2 earlier terms -- 2, 3, 6, 12, 18, 24, 48, 54, 96, 162, 192, 216, 384, 486, 768, 864, 1458, 1536, 1944, 3072, 3456, 4374, 6144, 7776, 12288, 13122, 13824, 17496, 24576, 31104, 39366, 49152, 55296, 69984, 98304, 118098, 124416
multiplicatively perfect: A007422 sum((div(n))) = G(2, 2, n) -- 1, 6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187
Narayana-Zidek-Capell: [T. V. Narayana, P. Capell] A002083 referring to integer, f(2n) = 2f(2n - 1), f(2n + 1) = 2f(2n) - f(n) -- 1, 1, 1, 2, 3, 6, 11, 22, 42, 84, 165, 330, 654, 1308, 2605, 5210, 10398, 20796, 41550, 83100, 166116, 332232, 664299, 1328598, 2656866, 5313732, 10626810, 21253620, 42505932, 85011864, 170021123, 340042246, 680079282, 1360158564
narcissistic: A005188 aka Armstrong or plus perfect, referring to n-digit integers = sum(G(2, n, d(i))) -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315, 24678050, 24678051, 88593477, 146511208, 472335975, 534494836, 912985153, 4679307774, 32164049650, ..., 115132219018763992565095597973971522401
*n-est: A072422 -- referring to Aronson-like sequence generated by the sentence, "N est prima littera in hic sententiam, doudevicesima littera in hic sententiam, quarta vicesima littera in hic sententiam, septima vicesima littera in hic sententiam, tertia quinquagentesima littera in hic sententiam ...." 1, 18, 24, 2753, 59, 62, 95, 98, 126, 132, 135, 149, 155, 170, 176, 184,  186, 191, 197, 212, 218, 221, 230, 251, 257, 260, 268, 271, 273, 289, 295,  298, 309, 311, 327, 333, 336, 356, 371, 377, 380, 389, 403, 418, 424, 427,  435, 449, 464, 470, 473, 478, 480
*neve: [prime:emirp::even:?] nonpalindromic even integer which is still even when reversed -- 24, 26, 28, 42,  46, 48, 62, 64, 68, 82, 84, 86,  204, 206, 208,  214, 216, 218, 224, 226, 228, 402, 404, 406, 408, 412, 416, 418, 422, 426, 428, 432, 436, 438, 442, 446, 448, 452, 456, 458, 462, 466, 468, 472, 476, 478, 482,486, 488, 492, 496, 498, 602
Newman-Shanks-Williams: [Morris Newman, Daniel Shanks, H. C. Williams] A002315 referring to integers, f(n) = 6f(n - 1) - f(n - 2); 1, 7, 41, 239, 1393, 8119, 47321, 275807, 1607521, 9369319, 54608393, 318281039, 1855077841, 10812186007, 63018038201, 367296043199, 2140758220993, 12477253282759, 72722761475561, 423859315570607, 2470433131948081
Nickerson: [R. S. Nickerson] referring to integer with digit i separated by i - 1 other digits -- 11, 3113, 531135, 11342324, 11413243, 23243114, 34231411, 41134232, 42324311
Niven: aka Harshad, A005349 referring to integers, f(n) = 0 (mod sum(d(i))) -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200, 201, 204
*nonacci: Fibonacci-like sequence but adding previous 9, f(n) = f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) + f(n - 5) + f(n - 6) + f(n - 7) + f(n - 8) + f(n - 9) -- 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2040, 4076, 8144, 16272, 32512, 64960, 129792, 259328, 518145, 1035269, 2068498, 4132920, 8257696, 16499120, 32965728, 65866496, 131603200, 262947072, 525375999, 1049716729
nonagonal: aka enneagonal, A001106 f(n) = n(7n - 5)/2 -- 0, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089, 1216, 1350, 1491, 1639, 1794, 1956, 2125, 2301, 2484, 2674, 2871, 3075, 3286, 3504, 3729, 3961, 4200, 4446, 4699, 4959, 5226, 5500, 5781,6069,6364
*non-cubes: f(n) = n + G(2, 1/3,  [(n + [G(2, 1/3, n}])] -- 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62,
non-octal: A057104 referring to integers with an 8 or 9 (they cannot be mistaken for octal integers) -- 8, 9, 18, 19, 28, 29, 38, 39, 48, 49, 58, 59, 68, 69, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 108, 109, 118, 119, 128, 129, 138, 139, 148, 149, 158, 159, 168, 169, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188
non-palindromic: A033868 referring to integers f(n) which is palindromic in no base b with 2 = b = n - 2 [elements of the sequence greater than 6 are prime Aab = f(b - 1) + a; G(2, 2, a) = G(2, 2, a - 1) + 2(a - 1) + 1)) -- 1, 2, 3, 4, 6, 11, 19, 47, 53, 79, 103, 137, 139, 149, 163, 167, 179, 223, 263, 269, 283, 293, 311, 317, 347, 359, 367, 389, 439, 491, 563, 569, 593, 607, 659, 739, 827, 853, 877, 977, 983, 997, 1019, 1049, 1061, 1187, 1213, 1237, 1367, 1433, 1439, 1447
Non-Rollman: [Hannah Rollman] A048992 referring to integers left after deleting any previous integer which has appeared as an earlier string -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 48, 49, 50, 54, 55, 57, 58, 59, 60, 65, 66, 68, 69, 70, 76, 77, 79, 80, 87, 88, 90, 99, 100, 101, 102, 103, 104, 105, 106, 107
*non-self: referring to integers, f(n) = N(x + sum(d(i))) -- 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 110, 112, 114, 116, 118, 120
non-squares: A000037 f(n) = n + [1/2 + G(2, 1/2, n)] --  2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
*number name as if in base 27: A072959 referring to integer resulting  from interpreting English name as if in Sallows' base 27 -- 11318, 15216, 10799546, 129618, 125258, 14118, 10211981, 2839691,  282506, 14729, 78236429, 299309045, 212445551527, 68884716992,  2457249197, 7503281492, 5427065792075, 55893641747,  150135668600, 299310469
*number name as if in base 36: A072922 referring to integer resulting  from interpreting English name as if in base 36 -- 1652100, 31946, 38760, 49537526, 732051, 724298, 36969, 47723135,  24375809, 1097258, 38111, 882492287, 1807948346, 2310701170991,  1242626638127, 33766692143, 62095095599, 1165465079087,  1137277763375, 1842973464623
oblong: aka promic or heteromecic, A002378 referring to integer, f(n) = n(n+1) -- 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162
octahedral: A005900 referring to integer, f(n) = (2G(2, 3, n) + n)/3 -- 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, 1469, 1834, 2255, 2736, 3281, 3894, 4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726, 13131, 14644, 16269, 18010, 19871, 21856, 23969, 26214, 28595, 31116, 33781, 36594, 39559, 42680
octal: A007094 referring to integers expressible in base 8, i. e., without 8 or 9 -- 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 100, 101, 102, 103, 104, 105
octogon: [Robert E. Smith] referring to integer with digits arrangable in octogon -- 1000000000000, 1000000000001, ..., 999999999999, 1000000000000000000000000000000000000, ...
octavan: [see octavan primes A006686] n = G(2, 8, x + G(2, 8, y) -- 2, 257, 512, 6817, 13122, 65537, 65792
*octonacci: A079262 referring to integers formed like Fibonacci numbers, but by adding previous 8, f(n) = f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) + f(n - 5) + f(n - 6) + f(n - 7) + f(n - 8) -- 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 255, 509, 1016, 2028, 4048, 8080, 16128, 32192, 64256, 128257, 256005, 510994, 1019960, 2035872, 4063664, 8111200, 16190208, 32316160, 64504063, 128752121, 256993248  
odd: A005408 referring to integers, f(n) = 2n + 1 -- 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131
oddly-even: referring to integer of the form 2n{2m + 1} -- 6, 10, 14, 18
odious: A000069 referring to integers with odd number of 1s in binary expansion -- 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 64, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 97, 98, 100, 103, 104, 107, 109, 110, 112, 115, 117, 118, 121, 122, 124, 127, 128
Padovan: A000931 referring to integers, f(n) = f(n - 2) + f(n - 3) -- 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625
palindromic: A0021130, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515
psquare root: A002778 1, 2, 3, 11, 22, 26, 101, 111, 121, 202, 212, 264, 307, 836, 1001, 1111, 2002, 2285, 2636, 10001, 10101, 10201, 11011, 11111, 11211, 20002, 20102, 22865, 24846, 30693, 100001, 101101, 10011, 111111, 200002,  798644, 1000001, 1001001
pal-lap: [I Love Me, Vol. I  by M. Donner (Algonquin Books, 1996) p. 268] generated by Palindromedes sieve: f(n) = n + R(n) or (n + R(n))+ R(n + R(n)) or (n + R(n))+ R(n + R(n)) +R((n + R(n))+ R(n + R(n))), etc. such that, f(n) is palindromic where if n = sum(G(2, i, 10)d(j)), and j = k, the reverse of n is R(n) =  sum(G(2, k - i), 10)d(k - 1)) -- 0 1 2 3 4 5 6 7 8 9 11 11 33 44 55 66 77 88 99 121 22 33 44 55 66 77 88 99 121 121 33 55 33 77 88 99 121 121 363 44 55 66 77 44 99 121 121 363 484 55 66 77 88 99 55 121 121 363 484 1111 66 77 88 99 55 121 363 484 1441 66 77 88 99 121 121 66 484 1111 4884 77 88 99 121 121 363 484 77 44044 88 99 121 121 363 484 1111 4884 88 8813200023188
panarithmic: A005153 referring to integers for which all k = f(n) are sums of distinct divisors of n -- 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168
 pancake: aka Lazy Caterer's or central polygonal integers, A000124 maximal integer of pieces formed when slicing a pancake with n cuts, n(n+1)/2 + 1 -- 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379
pandigital: referring to integer containing all ten digits at least once-- 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, 1023457968, 1023457986, 1023458679, 1023458697, 1023458769, 1023458796, 1023458967, 1023458976, 1023459678, 1023459687, 1023459768, 1023459786, 1023459867, 1023459876
*peban:[palindromic eban] 2, 4, 6, 44, 66, 2002, 4004, 6006, 44044, 66066, 2000002, 2002002, 4000004, 4004004, 6000006, 6006006, 44000044, 66000066,2000000002, 4000000004, 6000000006, 44000000044, 66000000066, 2000000000002, 2000002000002
Pell: A000129 refers to integers, [f(n - 1)/(G(2, 1/2, 2) - 1) +1/2], where f(0) = 1 -- 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, 18457556052, 44560482149
pentagonal: referring to integers, n(3n - 1)/2 -- 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151
pental: referring to integers expressible in base 5, i. e., without 5, 6, 7, 8, or 9 -- 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24,  30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 200
pentanacci: A001591 referring to integers, f(n + 1) = f(n) + ... + f(n - 4) -- 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, 786568, 1546352, 3040048, 5976577, 11749641, 23099186, 45411804, 89277256, 175514464, 345052351, 678355061, 1333610936
perfect: A000396 referring to integers equal to sum of proper divisors, n = sum(div(n)) -- 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176,
191561942608236107294793378084303638130997321548169216
Perrin: aka Ondrej, A001608 Such integers, f(n) = f(n - 2) + f(n - 3). so that f(p) = 0 (mod p) -- 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486, 644, 853, 1130, 1497, 1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 43721, 57918, 76725, 101639
*peven: [palindromic even] 2, 4, 6, 8, 22, 44, 66, 88, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 606, 616, 526, 636, 646, 656, 666, 676, 686, 696, 808, 818, 828, 838, 848, 858, 868, 878, 888, 898, 2002
*pfibonacci: [palindromic Fibonacci] 1, 2, 3, 5, 8, 55,
*pflimsy: [palindromic flimsy] 11, 22, 44, 55, 77, 88, 99
*phappy: [palindromic happy portmanteau] 1, 7, 44, 262, 313
*pheptagonal: [palindromic heptagonal] 0, 1, 7, 55, 616, 3553, 4774
*pheptal: [palindromic heptal] 0, 1, 2, 3, 4, 5, 6, 11, 22, 33, 44, 55, 66, 101, 111, 121, 131, 141, 151, 161, 202, 212, 222, 232, 242, 252, 262, 303, 313, 323, 333, 343, 353, 363, 404, 414, 424, 434, 444, 454, 464, 505, 515, 525, 535, 545, 555, 606, 616, 626, 636, 646, 656, 666, 1001
*phex: [palindromic hex] 1, 7, 919, 1081801, 1188811, 1946491
*phexagonal: [palindromic hexagonal] 1, 6, 66, 3003, 5995, 15051, 66066, 617716, 828828, 1269621, 1680861
*phexal: [palindromic hexal] 0, 1, 2, 3, 4, 5, 11, 22, 33, 44, 55, 101, 111, 121, 131, 141, 151, 202, 212, 222, 232, 242, 252, 303, 313, 323, 333, 343, 353, 404, 414, 424, 434, 444, 454, 505, 515, 525, 535, 545, 555, 1001, 1111, 1221, 1331, 1441, 1551, 2002
picture-perfect: A069942 R(n) = sum(R(div(n)) -- 6, 10311, 21661371, 1460501511, 7980062073, 79862699373, 798006269373
*poctal: [palindromic octal] 0, 1, 2, 3, 4, 5, 6, 7, 11, 22, 33, 44, 55, 66, 77, 101, 111, 121, 131, 141, 151, 161, 171, 303, 313, 323, 333, 343, 353, 363, 373, 404, 414, 424, 434, 444, 454, 464, 474, 505, 515, 525, 535, 545, 555, 565, 575, 606, 616, 626, 636, 646, 656, 666
*podd: [palindromic odd] 1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 303, 313, 323, 343, 353, 363, 373, 383, 393, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 909
practical: A007620 1, 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252, 260, 264, 270, 272, 276, 280, 288, 294, 300, 304, 306
prime:A000040 referring to integers with no positive divisors except 1 and n, div(n) = K(p)(1) -- 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271
*prime expansion: f(n) = sum(ip(i)) -- 1, 10, 100, 101, 1000, 1001, 10000, 10001, 10010, 10100, 100000, 100001, 1000000, 1000001, 1000010, 1000100, 10000000, 10000001, 100000000, 100000001, 100000010, 100000100, 1000000000, 1000000001, 1000000010, 1000000100, 1000000101, 1000001000, 10000000000,
primorial: A002110 referring to product of first n primes, p# = prod(p(i)) -- 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070
Proman: [palindromic Roman] 1, 2, 3, 5, 10, 19, 20, 30, 50, 100, 190, 200, 300, 500, 1000, 1900, 2000, 3000, 1000000, 2000000, 3000000
pseudoperfect: .A005835 referring to integers for which some set of proper divisors sums to n -- 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264
psmith: [palindromic smith] 4, 22, 121, 202, 454, 535, 636, 666, 1111, 1881
*psubemirp: [palindromic subemirp] 5, 6, 11, 55, 66, 272, 393, 404, 424, 434
*psubminimal:[palindromic subminimal] 0, 1, 2,4, 6, 9, 22, 44, 66, 88, 212, 353, 464
quartan: [see quartan prime, A002645] f(n) = f(x, y) = G(2, 4, x) + G(2, 4, y) --
 *quarter-cube: [square:quarter-square::cube:?] [G(2, 3, n)/4] --  0, 2, 6, 16, 31, 54, 85, 128, 182, 250, 332, 432,549, 686, 843,1024, 1228, 1458, 1714, 2000, 2315, 2662, 3041, 3456,3906, 4394, 4920, 5488, 6097, 6750, 7447, 8192, 8984, 9826, 10718, 11664, 12663, 13718, 14829, 16000
quarter-square: A002620 [G(2, 2, n)/4] -- 0, 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272, 289, 306, 324, 342, 361, 380, 400, 420, 441, 462, 484, 506, 529, 552, 576, 600
*quasi-narcissistic
*quasi-perfect
*quasi-powerful
RATS: [reverse-add-then-sort] A004000 1, 2, 4, 8, 16, 77, 145, 668, 1345, 6677, 13444, 55778, 133345, 666677, 1333444, 5567777, 12333445, 66666677, 133333444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, 556666667777, 1233333334444
Recaman: A005132 referring to integers in sequence such that f(0) = 0;  for n > 0, f(n) = f(n - 1) - n if that integer is positive and not already in the sequence, otherwise f(n) = f(n -1) + n -- 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26
refactorable: A033950 aka tau, referring to integer, n = 0 (mod #(div(n))) -- 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96, 104, 108, 128, 132, 136, 152, 156, 180, 184, 204, 225, 228, 232, 240, 248, 252, 276, 288, 296, 328, 344, 348, 360, 372, 376, 384, 396, 424, 441, 444, 448, 450, 468, 472, 480, 488, 492, 504, 516, 536
repdigit: A010785 referring to integers with repeated digits, f(n) = m(G(2, n, 10) - 1)/9 -- 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222
repunit: [Samuel Yates] A002275 -- f(n) = (G(2, n, 10) - 1)/9 -- 0, 1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111
*reven: [reverse-even] 2, 4, 6, 8, 1, 21, 41, 61, 81, 2, 12, 22, 42, 62, 82, 3, 23, 43, 63, 4, 24, 44, 64, 84, 5, 25, 45, 65, 85, 6, 26, 46, 66, 86, 7, 27, 47, 67, 87, 8, 28, 48, 68, 88, 9, 29, 49, 69, 89, 9, 29, 49, 69, 89, 1, 12, 14, 16, 18, 11, 112, 114, 116, 118, 12, 112  
reverse-and-add: [f(1) = 196] A006960 196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, 18211171, 35322452, 60744805, 111589511, 227574622, 454050344, 897100798, 1794102596, 8746117567, 16403234045, 70446464506, 130992928913, 450822227944, 900544455998, 1800098901007
ring: aka Riordan, A005043 referring to integers, f(n) = (n - 1)(2f(n - 1) + 3f(n - 2))/(n + 1) -- 1, 0, 1, 1, 3, 6, 15, 36, 91, 232, 603, 1585, 4213, 11298, 30537, 83097, 227475, 625992, 1730787, 4805595, 13393689, 37458330, 105089229, 295673994, 834086421, 2358641376, 6684761125, 18985057351
*rodd:[reverse odd] f(n) = R(2n + 1) -- 1, 3, 5, 7, 9, 11, 31, 51, 71, 91, 12, 32, 52, 72, 92, 13, 33, 53, 73, 93, 4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 5, 15, 35, 55, 75, 95, 16, 36, 56, 76, 96, 17, 37, 57, 77, 97, 18, 38, 58, 78, 98, 19, 39, 59, 79, 99, 101, 301, 501, 701, 901, 111
*Rollman: referring to integer not non-Rollman -- 12, 23, 31, 34, 41, 42, 45, 51, 52, 53, 54, 56, 61, 62, 63, 64, 65, 67, 71, 72, 73, 74, 75, 78,81, 82, 83, 84, 85, 86, 89, 91, 92, 93. 94, 95, 96, 97, 98,  
*Roman numeral as base-27: A073427 -- referring to integer transformed to Roman numeral then interpreted as if in  Sallows' base 27 -- 9, 252, 6813, 265, 22, 603, 16290, 439839, 267, 24, 657, 17748, 479205,  17761, 670, 18099, 488682, 13194423, 17763, 672, 18153, 490140,  13233789, 490153, 18166, 490491, 13243266, 357568191, 490155, 18168, 490545,  13244724,357607557
*Roman numeral as base-36: A073421 -- referring to integer transformed to Roman numeral then interpreted as if in  base 36 -- 18, 666, 23994, 679, 31, 1134, 40842, 1470330, 681, 33, 1206, 43434,  1563642, 43974, 1221, 43974, 1583082, 56990970, 1583095, 43987,  1583550, 57007818, 2052281466, 1583097, 43989, 1583622, 57010410,  2052374778, 57010423, 1583635
Ruth-Aaron: [Babe Ruth's lifetime home run record = 714, Hank Aaron's 715] A006145 CG(n, 1, div(i), div(i + 1)) = G(n, 1, div(n + 1), div(i + 2)); f(j) = n -- 5, 24, 49, 77, 104, 153, 369, 492, 714, 1682, 2107, 2299, 2600, 2783, 5405, 6556, 6811, 8855, 9800, 12726, 13775, 18655, 21183, 24024, 24432, 24880, 25839, 26642, 35456, 40081, 43680, 48203, 48762, 52554, 61760, 63665, 64232, 75140
s-ain't: A072886 referring to integer generated like the Aronson series from a generating sentence, "S ain't the second, third, fourth, fifth . . . letter of this sentence.". 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
Sarrus: A001567 pseudo-primes to base 2, Cn = f(n);G(2, n - 1, 2) = 1 - n[1/n] -- 341, 561, 645, 1105, 1387, 1729, 1905, 2047, 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911, 10261, 10585, 11305, 12801, 13741, 13747, 13981, 14491, 15709, 15841, 16705, 18705, 18721, 19951, 23001, 23377, 25761, 29341
*satyr: [sort-add-then-you-reverse] f(n) = R(sort(n) + n) -- 2, 4, 6, 8, 1, 21, 41, 61, 81, 11, 22, 42, 62, 82, 3, 23, 43, 63, 83, 4, 42, 44, 46,48, 5, 66, 77, 88, 99, 11, 112, 114, 116, 118, 66, 77, 88, 99, 11, 112, 123, 1, 134, 136, 138, 77, 88, 99, 11, 112
Scott: [Dana Scott] A048736  f(n) = (f(n - 2) + f(n - 1)f(n - 3))/f(n - 4) -- 1, 1, 1, 1, 2, 3, 5, 13, 22, 41, 111, 191, 361, 982, 1693, 3205, 8723, 15042, 28481, 77521, 133681, 253121, 688962, 1188083, 2249605, 6123133, 10559062, 19993321, 54419231, 93843471, 177690281, 483649942, 834032173, 1579219205, 4298430243
self: aka Columbian, A003052 referring to integers not expressible as the sum of an integer and its digit sum, f(n)  = N(k + sum(d(k))) -- 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310, 312, 323, 334, 345, 356, 367, 378, 389, 400, 411, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 514, 525
semi-Fibonacci: A030067 Kf(1) = 1; Kf(2x) = f(x); f(2x + 1) = f(x - 1) + f(x - 2) -- 1, 1, 2, 1, 3, 2, 5, 1, 6, 3, 9, 2, 11, 5, 16, 1, 17, 6, 23, 3, 26, 9, 35, 2, 37, 11, 48, 5, 53, 16, 69, 1, 70, 17, 87, 6, 93, 23, 116, 3, 119, 26, 145, 9, 154, 35, 189, 2, 191, 37, 228, 11, 239, 48, 287, 5, 292, 53, 345, 16, 361, 69, 430, 1, 431, 70, 501, 17, 518, 87, 605, 6, 611, 93
*semi-Tribonacci: [Fibonacci:semi-Fibonacci::Tribonacci:?]  Kf(0) = 0;K(1) = 1; Kf(2x);f(2x + 1) = f(2x) + f(2x - 1) + f(2n - 2) -- 0, 1, 1, 2, 1, 4, 2, 7, 1, 10, 4, 15, 2, 21, 7, 30, 1, 38, 10, 49, 4, 63, 15, 82, 2, 99, 21, 122, 7, 150, 30, 187, 1, 218, 38, 257, 10, 305, 49, 364, 4, 417, 63, 484, 15, 562, 82, 659, 2, 743, 99, 844, 21, 964, 122, 1107, 7, 1236, 150, 1393, 30, 1573, 187, 1790, 1, 1978, 218, 2197, 38, 2453, 257, 2748, 10, 3015, 305, 3330, 49, 3684, 364, 4097, 4, 4465, 417, 4886, 63, 5366, 484, 5913, 15, 6412, 562, 6989, 82, 7633, 659, 8374, 2, 9035743, 9780, 99, 10622, 844, 11565, 21, 12430, 964, 13415
*s-inner:  A072887 referring to integer not s-ain't -- 1, 9, 31, 36, 98, 107, 156, 164, 210, 221, 266, 312, 358, 365, 405, 415,  460, 467, 509, 519, 548, 556, 564, 566, 571, 577, 587, 598, 608, 613, 618,  623, 630, 641, 651, 661, 671, 673, 680, 686, 698, 711, 723, 730, 735, 742,  749, 762, 774, 792, 800
*slices of pi: A016062 -- digital expansion of pi such that f(n) > f(n-1) -- 3, 14, 15, 92, 653, 5897, 9323, 84626, 433832, 795028, 841971, 6939937, 51058209, 74944592, 307816406, 2862089986, 28034825342, 1170679821480, 8651328230664, 70938446095505, 82231725359408, 128481117450284, 1027019385211055
Smarandache: A002034 referring to smallest integer f(n) such that f(n)! = 0 (mod n) -- 1, 2, 3, 4, 5, 3, 7, 4, 6, 5, 11, 4, 13, 7, 5, 6, 17, 6, 19, 5, 7, 11, 23, 4, 10, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 5, 41, 7, 43, 11, 6, 23, 47, 6, 14, 10, 17, 13, 53, 9, 11, 7, 19, 29, 59, 5, 61, 31, 7, 8, 13, 11, 67, 17, 23, 7, 71, 6, 73, 37, 10, 19, 11, 13, 79, 6, 9, 41, 83, 7
Smith:[Harold Smith] referring to integer whose sum of digits equals digits of it factors -- 4, 22, 27,58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454,483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 867, 895, 913, 915, 922, 958, 985, 1085, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966
*sodd: [sort-odd] 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 12, 23, 25, 27, 29, 13, 33, 35, 37, 39, 14, 34, 45, 47, 49, 15, 35, 55, 57, 59, 16, 36, 56, 67, 69, 17, 37, 57, 77, 79, 18, 38, 58, 78, 89, 19, 39, 59, 79, 99, 11, 13, 15, 17, 19, 112, 123, 125, 127, 129, 113
split: A036382 referring to integer with non-trivial factorization n = ab, such that LCM[a, b] = 1, so that g(a) + g(b) = g(n), where g(x) is binary order of x, All even integers are split integers, except prime powers  -- 21, 33, 35, 39, 65, 69, 75, 77, 87, 91, 93, 105, 129, 133, 135, 141, 143, 145, 147, 155, 159, 161, 165, 175, 177, 183, 189, 195, 203, 217, 259, 261, 265, 267, 273, 275, 279, 285, 287, 291, 295, 297, 299, 301, 303, 305, 309, 315, 319, 321, 325, 327, 329, 339
square: A000290 referring to integers, f(n) = G(2, 2, n) -- 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849
square-free:A005117 f(n) = NG(2, 2, n) -- 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113
squarefull: A001694 referring to integers f(n) = 0 (mod G(2, 2, p)) -- 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, 529, 576, 625, 648, 675, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972, 1000
star: aka octagonal, A000567 referring to integers, f(n) = n(3n - 2) -- 0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936, 1045, 1160, 1281, 1408, 1541, 1680, 1825, 1976, 2133, 2296, 2465, 2640, 2821, 3008, 3201, 3400, 3605, 3816, 4033, 4256, 4485, 4720, 4961, 5208, 5461
Stern: A005230 referring to integers for which f(1) = 1 and f(n + 1) is the sum of the x preceding terms, where x(x - 1)/2 < n = x(x + 1)/2 --  1, 1, 2, 3, 6, 11, 20, 40, 77, 148, 285, 570, 1120, 2200, 4323, 8498, 16996, 33707, 66844, 132568, 262936, 521549, 1043098, 2077698, 4138400, 8243093, 16419342, 32706116, 65149296, 130298592, 260075635, 519108172, 1036138646, 2068138892, 4128034691
strobogrammatic: aka vertically palindromic A000787 -- 0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, 916, 986, 1001, 1111, 1691, 1881, 1961, 6009, 6119, 6699, 6889, 6969, 8008, 8118, 8698, 8888
*subcarmichael: [factorial:subfactorial::Carmichael:?] 206, 407, 636, 907, 1038, 2428, 3278, 3894, 5828, 10794, 15098, 17164, 19363, 23083, 23534, 27724, 37193, 42645, 46433, 59744, 63305, 69331, 92927   
*subcube: [factorial:subfactorial::cube:?] [G(2, 3, n)/e + 1] -- 0, 3, 10, 24, 46, 79, 126, 188, 268, 368, 490, 636, 808, 1009, 1242, 1507, 1807, 2145, 2523, 2943, 3407, 3917, 5086, 5748, 6466, 7241, 8076, 8972, 9933, 10959, 12055, 13220, 14459, 15773, 171164, 18634
*subdecacci: [factorial:subfactorial::decacci:?] 0, 1, 1, 3, 6, 12, 24, 47, 94, 188, 376, 752, 1504, 3006, 6010, 12013, 24015, 48007, 95967, 191839, 383489, 766602, 1532452, 3063401, 6123795, 12241580, 24471146, 48918277
*subdemlo: [factorial:subfactorial::Demlo:?] 0, 45, 4533, 454081, 45416307, 4541712413, 454172058760, 45417214051093, 4541721486860290
*subdodecahedral: [factorial:subfactorial::dodecahedral:?] 0, 7, 31, 81, 167, 300, 489, 745, 1076, 1494, 2007, 2627, 3362, 4223, 5220, 6363, 7661, 9125, 10764, 12589, 14609, 16834, 19275, 21940, 24841, 27987
*subdowling:[factorial:subfactorial::Dowling:?] 0, 1, 5, 53, 681, 10140, 174274, 3417746, 74953683, 1807204214, 47374658135, 1340216472714
*subemirp: [factorial:subfactorial::emirp:?] 5, 6, 11, 14, 26, 27, 29, 36, 39, 55, 58, 61, 66, 73, 114, 124, 128, 132, 143, 258, 261, 270, 272, 273, 276, 280, 283, 334, 345, 346, 351, 356, 357, 362, 365, 371, 376, 379, 390, 393, 401, 404, 406, 408, 423, 424, 434, 439
*subeuler: [factorial:subfactorial::Euler:?] 0, 1, 2, 6, 22, 100, 510, 2929, 18586, 130153, 994292,
subfactorial: aka rencontres, A000166 derangements or permutations of n elements with no fixed points, f(0) = 1, f(n) = [n!/e + ½] for n > 0 -- 1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570,
176214841, 2290792932, 32071101049, 481066515734, 7697064251745, 130850092279664, 2355301661033953, 44750731559645106, 895014631192902121, 18795307255050944540
*subfortunate:  [factorial:subfactorial::fortunate:?] 1, 2, 3, 5, 8, 6, 7, 8, 14, 22, 25, 22, 26, 17, 39, 22, 22, 40, 33, 38, 29, 56, 72, 37, 38, 82, 82, 47, 82, 70, 60, 84, 237, 88, 58, 61, 161, 88, 73, 70, 73, 141, 86, 276, 115, 284, 223, 115, 141, 108, 163, 122, 104, 102, 100, 148, 113, 122
*subfranel: {factorial:subfactorial::Franel:?] 0, 1, 4, 20, 127, 828, 5586, 38613, 271923, 1942746, 14040215, 102423489, 753021404, 5572764973, 41474148184, 310169073798, 2329522847111, 17561580656514
*subharmonic: [factorial:subfactorial::harmonic:?] 0, 2, 10, 52, 99, 182, 247, 603, 1093, 2281, 2990, 3013, 6843, 6850, 10244, 11125, 12052, 20550, 38872, 43336, 61583, 63864, 87375, 89049, 122371, 132569, 198434, 255868, 267147, 277190, 349845, 400720, 522860, 566431
*subJacobsthal-Lucas: [factorial:subfactorial:: subJacobsthal-Lucas:?] 0, 2, 3, 6, 11, 24, 47, 95, 188, 377, 753, 1507, 3013, 6028, 12054, 24110, 48218, 96438, 192874, 385750, 771499, 1542999, 3085996, 6171993, 12343985, 24687972, 49375942, 98751886, 197503771, 395007543, 790015084, 1580030169, 3160060337, 6320120675, 12640241349, 25280482700, 50560965398, 101121930797, 202243861594, 404487723188, 808975446375,
*sublah: [factorial:subfactorial::Lah:?] [(n - 1)n!/2e + 1/2] -- 0, 2, 13, 88, 662, 5562, 51915, 533984, 6007324, 73422850, 969181625, 13744757592, 208462156818, 3367465610138, 57727981888087, 1046800738237310
*submarkoff: [factorial:subfactorial::Markoff:?] 0, 1, 2, 5, 11, 13, 33, 62, 71, 86, 159, 224, 362, 487, 588, 1066, 1538, 2112, 2379, 2782, 3339, 4027, 5408, 10542, 12310, 13857, 15915, 18998, 22886, 27600, 35521, 49714, 71746, 72258, 108409, 156860, 183716, 189174, 237657
*subminimal: [factorial:subfactorial::minmal:?] 0, 1, 1, 2, 4, 6, 9, 13, 18, 22, 24, 44, 53, 66, 71, 88, 132, 212, 265, 309, 331, 353, 377, 464, 477, 618, 927, 1059, 1130, 1324, 1507, 1854, 1907, 2318, 2384, 2472, 2781, 3390, 3708
*submodest: [factorial:subfactorial::modest:?] 5, 7, 8, 10, 11, 14, 17, 18, 22, 18, 22, 25, 29, 33, 38, 40, 41, 49, 76, 77, 78, 80, 82, 86, 98, 110, 114, 120, 123, 147, 149, 151, 152, 154, 155, 159, 160, 163, 171, 184, 187, 188, 189, 196, 200, 204, 220, 224, 225, 227, 229, 231
*subpeban: [factorial:subfactorial::peban:?] 1, 2, 16, 24, 736, 1473, 2209, 16203, 24304, 735760, 736495, 1471519, 1472991, 2207279, 2209486, 16186712, 24280067, 735758883, 1471517766, 2207276649   
*subperfect: [factorial:subfactorial::perfect:?] 2, 10, 182, 2990, 12342479, 3160036228, 50560868961, 848272237263603328
*subphexagonal: [factorial:subfactorial:phexagonal:?] 0, 2, 24, 1105, 2205, 5537, 24304, 227245, 304909, 467067, 618354
*subpodd: [factorial:subfactorial::podd:?] 0, 1, 2, 3, 3, 4, 12, 20, 28, 36, 37, 41, 45, 48, 52, 56, 59, 63, 67, 70, 111, 115, 119, 123, 126, 130, 134, 137, 141, 145, 186, 189, 193, 197, 200, 204, 208, 212, 215, 219
*subprimorial: [factorial:subfactorial::primorial:?] A079266 [n#/e + 1/2] -- 0, 1, 2, 11, 77, 850, 11047, 187806, 3568317, 82071280, 2380067130, 73782081030, 2729936998040, 111927416922654, 4812878927674130
*subsquare: [G(2, 2, n)/e + 1/2] -- 0, 1, 3, 6, 9, 13, 18, 24, 30,37, 45, 53, 62, 72, 83, 94, 106, 119, 133, 147, 162, 178, 195, 212, 230, 249, 268, 288, 309, 331, 354, 377, 401, 425, 451, 477, 504, 531, 560, 589, 618, 649, 680, 712, 745, 778, 813, 848, 883, 920, 957
*suburban: A072955 referring to integer without b, r, s or u -- 1, 2, 5, 8, 9, 10, 11, 12, 15, 18, 19, 20, 21, 22, 25, 28, 29, 50, 51, 52, 55,  58, 59, 80, 81, 82, 85, 88, 89, 90, 91, 92, 95, 98, 99, 1000000, 1000001,  1000002, 1000005, 1000008, 1000009, 1000010, 1000011, 1000012, 1000015,1000018,1000019,1000020
suitable: aka convenient or idoneal, A000926 referring to integers n such that p odd,, having unique representation as G(2, 2, x) + nG(2, 2, y), x, y = 0, (x, y) = 1, implies p prime. -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93, 102, 105, 112, 120, 130, 133, 165, 168, 177, 190, 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, 1848
super-abundant: A004394 referring to integer n such that prod(d(n)/n)  >  G(n, 1, d(i)/(i), (d(i+1)/(i+1)) for all x < n -- 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800
*supercake: [factorial:superfactorial::cake:?] referring to the product of previous cake integers, f(n) = G(n, 1, (C(i + 1, 3) + i + 1, C(i + 2, 3) + i + 2) -- 1, 2, 8, 64, 960, 24960, 1048320, 67092480, 6239600640, 811148083200, 142762062643200, 3140765378150400, 939088848066969600
*supercats: 2, 6, 408, 5304, 1177488, 41212080, 1030302000, 389454156000, 4283995716000, 5286450713544000
*supercomposite: [factorial:superfactorial::composite:?] referring to integers which are the product of first n composite integers -- 1, 4, 24, 192, 1728, 17280, 207360, 2903040, 43545600, 696729600, 12541132800, 250822656000, 5267275776000, 115880067072000, 2781121609728000, 69528040243200000, 1807729046323200000, 48808684250726400000, 1366643159020339200000
*supercube: [factorial:superfactorial::cube:?] referring to product of previous cubes, f(n) = prod(G(2, 3, n)) -- 1, 8, 216, 13824, 1728000, 373248000, 128024064000, 65548320768000, 47784725839872000, 47784725839872000000, 63601470092869624000000
*supercurious: [factorial:superfactorial::curious:?] 1, 5, 30, 750, 57000, 21432000, 13395000000, 125591520000000, 11381731500000000000
*supereuler: [factorial:superfactorial::Euler:?] 1, 2, 10, 160, 9760, 2654720, 3676787200, 29178983219200
*supereven: [factorial:superfactorial::even:?] f(n) = prod(2n) -- 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200, 81749606400, 1961990553600, 51011754393600, 142832913020800
superfactorial: A000178 referring to product of first n factorials, f(n) = prod(n!) -- 1, 1, 2, 12, 288, 34560, 24883200, 125411328000, 5056584744960000, 1834933472251084800000, 6658606584104736522240000000,
265790267296391946810949632000000000
*superfortunate: {factorial:superfactorial::fortunate:?] referring to product of previous fortunate integers, 3, 15, 105, 1365, 31395, 533715, 10140585, 233233455, 8629637835, 526407907935, 35269329831645, 2151429119730350, 152751467500854496, 7179318972540161024, 768187130061797179392, 45323040673646030716928
*superJacobsthal-Lucas: [factorial:superfactorial:: subJacobsthal-Lucas:?] 1, 5, 35, 595, 18445, 1198925, 152263475, 39131713075, 19996305381325
*superménage: [factorial:superfactorial:: ménage:?] referring to product of previous non-zero menage integers -- 3, 39, 3237, 1916304, 9238501584, 406300061162736, 180646289093747539968
*supermersenne: [factorial:superfactorial::Mersenne:?] referring to product of previous Mersenne integers, f(n) = prod(G(2, p, 2) - 1) -- 3, 21, 651, 82677, 169239819, 1386243357429, 181696303101576448
*superpancake: [factorial:superfactorial::pancake:?] referring to product of previous pancake integers, f(n) = prod(n(n + 1)/2 + 1) -- 2, 8, 56, 616, 9856, 216832, 6288128, 232660736, 10702393856, 599334055936, 40155381747712, 3172275158069250, 291849314542370816
*superpodd: [factorial:superfactorial::podd:?]  f(n) = prod(2n + 1) = prod(R(2n + 1)) -- 1, 3, 15, 105, 945, 10395, 343035, 18866925, 1452753225, 143822569275, 14526079496775, 1612394824142020     
*superprimorial: A079264 referring to product of first n primorials, f(n) = prod(#n) -- 1, 2, 12, 360, 75600, 174636000, 5244319080000, 2677277333530800000
*supersmarandache: [factorial:superfactorial::Smarandache:?] referring to product of Smarandache sequence integers -- 2, 8, 32, 160, 480, 3360, 13440, 80640, 403200, 4435200, 17740800, 230630400, 1614412800, 8072064000, 137225088000, 823350528000, 15643660032000, 7821830016000, 547528101120000, 6022809112320000, 138524609583360000
*supersquare: [factorial:superfactorial::square:?] referring to product of previous squares, f(n) = prod(G(2, 2, n) = G(2, 2, n!) -- 1, 4, 36, 576, 14400, 518400, 25401600, 1625702400, 131681894400, 13168189440000, 1593350922240000, 220442532802560000, 38775788043632640000, 7600054456551997440000
*supervampire: [factorial:superfactorial::vampire:?] referring to product of previous vampire integers -- 126, 19278, 13263264, 15995496384, 20074347961920, 25293678432019200, 35284681412666785792
*taliban: A072954 referring to integer without a, i, l or t -- 0, 1, 4, 7, 64, 100, 101, 104, 107, 343, 401, 404, 407, 700, 701, 704, 707
ternary sieved: A007951 delete successively every G(2, n, 3)th integer -- 1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22, 23, 25, 28, 29, 31, 32, 34, 35, 37, 38, 41, 43, 46, 47, 49, 50, 52, 55, 56, 58, 59, 61, 62, 64, 65, 68, 70, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 88, 91, 92, 95, 97, 98, 100, 101, 103, 104, 106, 109, 110, 112, 113, 115, 116, 118
*t-est: A072423 referring to integer generated by generating sentence, "T est prima et quarta et undecima et sexima decima et nona decima et nona vicesima ... littera in hic sententiam." -- 1, 4, 11, 16, 19, 29, 33, 42, 56, 70, 71, 74, 77, 87, 105, 109, 121, 128, 132,  142, 151, 161, 166, 171, 181, 185, 192, 202, 207, 212, 219, 227, 234, 251,  258, 261, 276, 283, 291, 313, 320, 343, 350, 366, 375, 382, 401, 408, 412,  427, 434, 443, 455, 462
tetrahedral: A000292 referring to integers, f(n) = (n + 1)(n + 2)(n + 3)/6 -- 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180
Tetranacci: A001630 referring to Fibonacci-like integers, but added 4 at a time, f(n) = f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) -- 0, 0, 1, 2, 3, 6, 12, 23, 44, 85, 164, 316, 609, 1174, 2263, 4362, 8408, 16207, 31240, 60217, 116072, 223736, 431265, 831290, 1602363, 3088654, 5953572, 11475879, 22120468, 42638573, 82188492, 158423412, 305370945, 588621422, 1134604271
*semi-Tetranacci: [Fibonacci:semi-Fibonacci::Tetranacci:?] KCn = 2x;f(n) = f(x);Cn = 2x + 1;f(n) = f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) -- 0, 0, 1,
*toscodicity: A072420 minimum number of steps needed to transform the integer into 153 by either operation of the triple-or-sum-of-cube-of-digits (TOSCOD) operator, f(n) = #(A(3n)(G(n, 0, G(2, 3, d(i), d(i + 1)))) < #(A(3n)(G(n, 0, G(2, 3, d(j), d(j + 1)))) -- 4, 4, 3, 5, 4, 3, 5, 4, 3, 4, 5, 4, 4, 4, 3, 7, 2, 2, 4, 4, 4, 6, 4, 3, 6, 5, 2, 7, 5, 3,  4, 4, 5, 5, 3, 3, 5, 5, 3, 5, 4, 3, 5, 5, 2, 6, 5, 6, 6, 4, 1, 6, 3, 2, 6, 5, 3, 6, 3, 3,  7, 5, 3, 6, 5, 5, 4, 4, 3, 5, 2, 2, 5, 5, 3, 4, 5, 4, 5, 4, 2, 7, 7, 6, 6, 4, 4, 5, 4, 3,  4, 5, 3, 6, 3, 3, 5, 4, 4, 4
tree: [Robert E. Smith] referring to integer with G(2, 2, n) digits arrangable in rows of 2n + 1 digits like a Christmas tree -- 1000, 1001, ..., 9999, 100000000, 100000001, ...
triangular: A000217 referring to integers, f(n) = n(n + 1)/2 -- 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431
Tribonacci: A000073 referring to Fibonacci-like integers, f(n) = f(n - 1) + f(n - 2) + f(n - 3) -- 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591, 29249425, 53798080, 98950096, 181997601, 334745777
triperfect: A005820 referring to integers for which the sum of divisors of n is 3n, CG(div(n), 1, div(i), div(i + 1)) =3n);f(j)) = n -- 120, 672, 523776, 459818240, 1476304896, 51001180160
triple factorial: A007661 referring to integers, n!!! = f(n) = nf(n - 3).-- 1, 1, 2, 3, 4, 10, 18, 28, 80, 162, 280, 880, 1944, 3640, 12320, 29160, 58240, 209440, 524880, 1106560, 4188800, 11022480, 24344320, 96342400, 264539520, 608608000, 2504902400, 7142567040, 17041024000, 72642169600
truncated cube: A005911 referring to integers, f(n) = G(2, 3, 3n + 1) - 8n(n + 1)(n + 2)/6 = 77G(2, 3, n)/3 + 23G(2, 2, n) + 19n/3 + 1 -- 1, 56, 311, 920, 2037, 3816, 6411, 9976, 14665, 20632, 28031, 37016, 47741, 60360, 75027, 91896, 111121, 132856, 157255, 184472, 214661, 247976, 284571, 324600, 368217, 415576, 466831
truncated square: A005892 referring to integers, f(n) = 7G(2, 2, n) + 4n + 1 -- 1, 12, 37, 76, 129, 196, 277, 372, 481, 604, 741, 892, 1057, 1236, 1429, 1636, 1857, 2092, 2341, 2604, 2881, 3172, 3477, 3796, 4129, 4476, 4837, 5212, 5601, 6004, 6421, 6852, 7297, 7756, 8229, 8716, 9217, 9732, 10261, 10804, 11361, 11932
*turban: A072956 without letters r, t, or u.-- 1, 5, 6, 7, 9, 11, 1000000, 1000001, 1000005, 1000006, 1000007,  1000009, 1000011, 5000000, 5000001, 5000005, 5000006, 5000007,  5000009, 5000011, 6000000, 6000001, 6000005, 6000006, 6000007,  6000009, 6000011, 7000000, 7000001
*uban: [e:u:eban:?] 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45. 46. 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, ..., 399, 500, ...
Ulam: A002858 referring to integer which is uniquely the sum of 2 earlier terms -- 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, 57, 62, 69, 72, 77, 82, 87, 97, 99, 102, 106, 114, 126, 131, 138, 145, 148, 155, 175, 177, 180, 182, 189, 197, 206, 209, 219, 221, 236, 238, 241, 243, 253, 258, 260, 273, 282, 309, 316, 319, 324, 339
Ulysses: [Ulysses by James Joyce, see A054382, [log(n)]] referring to integer like 369,693,100-digit G(2, 2, 9, 9) = G(2, G(2, 9, 9), 9) = G(2, 387420489, 9), f(n) = G(2, 2, n, n) -- 1, 16, 7625597484987, c. 1.3407807G(2, 154, 10), c. 1.9110G(2, 2185, 10), c. 2.6591G(2, 36036, 10), c. 3.7598G(2, 695975, 10), c. 6.0145G(2, 15151336, 10), c. 4.2812G(2, 369693100, 10), G(2, 10000000000, 10)
*subulysses: [factorial:subfactorial::Ulysses:?] 0, 6, 2805300541375, c. 4.932456888G(2, 153, 10)
unbalanced: 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87
unlucky: 2, 4, 5, 6, 8, 10, 11, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 32, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 70, 71, 72, 74
unsuitable: 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18,19, 20, 21, 22, 23, 24, 25, 26,27,28, 29, 30, 31, 32, 33, 34, 35,36, 37, 38,39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78 79, 80, 81, 82
*urban: A072957 referring to integer without r or u -- 1, 2,5, 6,7, 8,9, 10,11, 12,15, 16,17, 18,19, 20, 21, 22, 25, 26, 27, 28, 29, 50, 51, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 1000000, 1000001, 1000002
*useless: A073418 -- referring to integer without e, s or u -- 2, 40, 42, 50, 52, 90, 92, 200, 240, 242, 250, 252, 290, 292, 2000000,  2000002, 2000040, 2000042, 2000050, 2000052, 2000090, 2000092,  2000200, 2000240, 2000242, 2000250, 2000252, 2000290, 2000292,  40000000, 40000002, 40000040
vampire: A020342 referring to integer n which has a factorization using n's digits (e.g. 1395 = 31(9)5) -- 126, 153, 688, 1206, 1255, 1260, 1395, 1435, 1503, 1530, 1827, 2187, 3159, 3784, 6880, 10251, 10255, 10426, 10521, 10525, 10575, 11259, 11439, 11844, 11848, 12006, 12060, 12384, 12505, 12546, 12550, 12595, 12600, 12762, 12768, 12798, 12843, 12955, 12964
Vinogradov: referring to odd integer which is sum of 3 different primes, f(n) = 2i + 1 = p(i) + p(j) + p(k) -- 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37
Wedderburn-Etherington: A001190 referring to binary rooted trees (every node has out-degree 0 or 2) with n endpoints (and 2n - 1 nodes in all), f(2n - 1) = f(1)f(2n - 2) + f(2)f(2n - 3) + ... + f(n - 1)f(n)), f(2n) = f(1)f(2n - 1) + f(2)f(2n - 2) + ... + f(n - 1)f(n + 1) + f(n)(f(n) + 1)/2) -- 0, 1, 1, 1, 2, 3, 6, 11, 23, 46, 98, 207, 451, 983, 2179, 4850, 10905, 24631, 56011, 127912, 293547, 676157, 1563372, 3626149, 8436379, 19680277, 46026618, 107890609, 253450711, 596572387, 1406818759, 3323236238, 7862958391
weird: A006037 referring to integers abundant but not pseudoperfect -- 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17990, 18410, 18830, 18970, 19390, 19670
Woodall: aka Riesel, A003261 referring to integers, nG(2, n, 2) - 1 -- 1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519, 44040191, 92274687, 192937983, 402653183, 838860799, 1744830463, 3623878655, 7516192767
*worthless numbers: A073419 referring to integer without h, o, r, t, or w -- 5,6, 7, 9, 11, 500, 505, 506, 507, 509, 511, 600, 605, 606, 607, 609, 611,  700, 705, 706, 707, 709, 711, 900, 905, 906, 907, 909, 911, 5000000, 5000005, 5000006, 5000007, 5000009, 5000011, 6000000, 6000005, 6000007, 6000009, 6000011