Sequences

Some of the sequences referenced in the club's other pages are named and further explained here. Some, those with an "A number", are officially recognized by the On-line Encyclopedia of Integer Sequences, OEIS. Those with an asterisk were submitted by members of the André Joyce Fan Club.

aban: [e:a::eban:?] referring to integers without an "a" -- 0, 1, 2, 3, ... , 999, 1000000, 1000001, ... , 1000999, 2000000, 2000001, ... , googol, ..., googolplex, ...

Abntu: ["ab-'n-too", Bantu (ban two) alphome] A072809 alphadigital Bantu, with digits in alphabetical order, namely, 8, 5, 4, 9, 1, 7, 6, 3, 0

acci: [nonacci backformation] integer not nonacci, A104144, a(n) ≠ a(n - 1) + a(n - 2) + a(n - 3) + a(n - 4) + a(n - 5) + a(n - 6) + a(n - 7) + a(n - 8) + a(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 a(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, ...

all-base inventory: inventory of n in all bases n to one -- 1, 10, 11, 10, 11, 111, 10, 11, 100, 1111, 10, 11, 12, 101, 11111, 10, 11, 12, 20, 110, 111111, 10, 11, 12, 13, 21, 111, 1111111, 10, 11, 12, 13, 20, 22, 1000, 11111111, 10, 11, 12, 13, 14, 21, 100, 1001, 1111111111, 10, 11, 12, 13, 14, 20, 22, 101, 1010, 1111111111, 10, 11, 12, 13, 14, 15, 21, 23, 102, 1011, 11111111111, 10, 11, 12, 13, 14, 15, 22, 24

almost Beethoven: digital expantion of Beethoven -- 2, 1, 3, 6, 5, 5, 6, 0, 6, 7, 6, 8, 9, 2, 9, 3, 1, 2, 5

*almost-perfect: A079718 digital expansion of perfect numbers

alphadigital: 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, ...

*anti-numberdromes, odd-digited:, A093472

*Babylonian reciprocal: ["igibum"] A094086 number which when multiplied by nth ugly number gives a power of sixty, a(n) = g(2, [log(n)/log(60)], 60)/A51037(n)

*Bantu: [ban two] A052404 referring to integer without 2

Begöl: [alphadigital Göbel] 1, 2, 3, 5, 10, 82, 541, 5320, 8855110, 591777663220, 5544911176666332220000

beta Centauri: [alpha:alpha Centauri::beta:?] tridigital expansion of p - 3, a(n) = [g(2, (3n + 3)(p -3), 10] - [g(2, 3n, 10)(p - 3)] -- 141, 592, 653, 589, 793, 238, 462, 643

reversed binary in decimal: a(n) = R(n (base 2)) (base 10) -- 0, 1, 1, 3, 2, 5, 2, 7, 1, 9, 5, 13, 3, 11, 7, 15, 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27, 7, 23, 15, 31, 1, 33, 17, 49, 9, 41, 25, 57, 5, 37, 21, 53, 13, 45, 29, 61, 3, 35, 19, 51, 11, 43, 27, 59, 7, 39, 23, 55, 15, 47, 31, 63, 1, 65, 33, 97, 17, 81, 49, 112, 9, 73, 41, 105, 25, 89, 57, 121, 5, 69, 37, 101, 21, 85, 53, 117, 13, 77, 45, 109, 29, 93, 61, 125, 3, 67, 35, 99, 19

biographical: referring to integer which tallies one or more other integers' digits left-to-right from n zero a(n) = #(d(n) = 0)g(2, d(n\n), 10), 10 + #(d(n) = 1)g(2, (d(n) - 1), 10) + ... + #(d(n) = 9) -- 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 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

bipolar: with only minimum and maximum digits, a(n) = 9Sg(2, a, 10) > , where i = 0 or 1 -- 90, 900, 909, 990, 9000, 9009, 9090, 9099, 9900, 9909, 9990, 90000, 90009, 90090, 90099, 90900, 90909, 90990, 90999, 99000, 99009, 99090, 99099, 99900, 99909, 900000, 900009, 900090, 900099

*Caliban: [a:aban::cali:?] A072958 referring to integer without a, c, i or l

*cancrine: A081365 word-palindrome number

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, modified: A072761 referring to modified Collatn sequence allowing change of x to 3x + 1 even when x = 2n

consonant-tailed: NA79741 integer with name ending in consonant -- 4, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 24, 26, 27, 28, 34, 36, 37, 38, 44, 46, 47, 48, 54, 56, 57, 58, 64, 66, 67, 68, 74, 76, 77, 78, 84, 86, 87, 88, 94, 96, 97, 98, 100, 104, 106, 107, 108, 110, 111, 113, 114, 115, 116, 117, 118, 119, 124, 126, 127, 128, 134, 136, 137

cubefull: [square:squarefull::cube:?, Paul Erdos and G. Szekeeres] A036966 referring to integer divisible by a prime cubed, a(n) = 0 (mod g(2, 3, p)

*curvaceous: A072960 referring to integer written with curves only, i. e., with 0, 3, 6, 8 or 9

*curvilinear: A072961 referring to integer which is both curved and linear, i. e., 2 or 5

dear: A2045020 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: A245019 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,

dearest: A0245018 with only 7s, 8s, and 9s -- 789, 798, 879, 897, 978, 987, 7789, 7798, 7879, 7889, 7897, 7898, 7899, 7978, 7987, 7989, 7998, 8779, 8789, 8797, 8798, 8799, 8879, 8897, 8977, 8978, 8979, 8987, 8997,

decacci: [Roger Bagula and Gary W. Adamson] A122265 Fibonacci-like sequence but adding previous 10, a(n) = a(n - 1) + a(n - 2) + a(n - 3) + a(n - 4) + a(n - 5) + a(n - 6) + a(n - 7) + a(n - 8) + a(n - 9) + a(n - 10)

decinary reversal: [David W. Wilson] A030101 alternating between base 2 and base 10 reversing between a(n + 1) = R(a(n)(base 2)) (base 10)

*DENEAT: A073053 referring to integer generated by application of DENEAT (digits-even-not-even-and-total) operator, a(n) = 100(#(d(x))) + 10(#(d(y)) + #(d(n)) where d(x) = 0 (mod 2) and d(y) = 1 (mod 2)

*deneaticity: A073054 referring to number of applications of DENEAT (digits-even-not-even-and-total) operator needed to reduce n to 123, a(n) = #(DENEAT(n))

*Diephi: [Diep + phi] A093473 next n digits of phi

digital power: [addition:exponentiation::digital sum:?, Reinhard Zumkeller] A075877 a(n) = Pd(i), g(2, d(i + 1), where n = Sg(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:?, R. Miller] A007954 a(n) = P(d(i)), where n = Sg(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,

d-ish: containing a "d" -- 100, 101, 102, 103, 104, 105, 106, 107, ,,,, 999999, 1000100, 1000101

*dodecahedral gnomic: A093485 a(n) = n(3n - 1)(3n -2)/2 - (n - 1)(3(n -1) -1)(3(n - 1) - 2)/2

double-header: integer with first two digits identical, a(n) = 11a(g(2, [l0(b - 2)], 10) + b, a < 10 -- 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 112, 113, 114, 115, 116, 117, 118, 119, 220, 221, 223, 224, 225, 226, 227, 228, 229, 330, 331, 332, 334, 335, 336,337, 338, 339, 440

*double primorial: [factorial:primorial::double factorial:?] A079078 n## = p(i)p(i - 2)##; ((2n)## = Π(p(2i)) and (2n + 1)## = Π(p(2i + 1)), where p(n) = nth prime

dufactorial: a(n) = (n!)! A205022-- 1, 2, 720, 620448401733239439360000, 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000

*Eckover: [pi:e::Pickover:?] A093648 decimal place of first n digits of pi in e -- 38, 1862, 3918

Eelru: [alphadigital Euler] 1, 1, 1, 2, 5, 16, 722, 8513, 9763, 55120, 597332, 5776220, 85663222, 899911630, 5911773320, 55499111132, 854997663220, 88444499117733320, 88888591132220, 885511777333220, 8554449991163200, 88449991177633330

emdost: [alphadigital modest] 13, 91, 32, 62, 92, 93, 46, 49, 59, 96, 97, 89, 130, 910, 111, 133, 991, 320, 620,

empowered [Reinhard Zumkelle] n = abcdef..., a(n) = (...(((((a^b)^c)^d)^e)^f)...

evil: A001969 with even number of ones in binary

exponential primorial: A140319 a(n) = g(p(n - 1), (2, 0), -1, p(n)) -- 1, 2, 9, 1953125, 1.286479g(2, 1.650582g(2, 6, 10)

faketorial: a(a(n)) = (n!)! -- 1, 1, 2, 6, 7, 8, 720, 721, 722, 723, 724, 726, 727, 728,

9006084097

flawed: NA73417 integer with a, f, l or w -- 2, 4, 5, 11, 12, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 64, 65, 72, 74, 75, 82, 84, 85, 92, 94, 95, 102, 104, 105, 111, 112, 120, 121, 122

*flawless: A073417 referring to integer without a, f, l or w

*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 ..."

godless: without d, g or o -- 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 17, 19, 20, 23, 25, 26, 27, 29, 30, 33, 35, 36, 37, 39, 50, 53, 55, 56, 57, 59, 60, 63, 65, 66, 67, 69, 70, 73, 75, 76, 77, 79, 90, 93, 95, 96, 97, 99

godly: with d, g or o -- 0, 1, 2, 4, 8, 14, 18, 21, 22, 24, 28, 31, 32, 34, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 58, 61, 62, 64, 68, 71, 72, 74, 78, 91, 92, 94, 98, 100, 101, 102, 103

gogo: a(n) = g(3, 2, n) -- 1, 4, 27, 256, 46656, 16777216, 8916100448256, 11112006825558016, 437893890380859375, 18446744073709551616, 827240261886336764177, 39346408075296537575424, 1978419655660313589123979, 104857600000000000000000000, 5842587018385982521381124421

gogoo: a(n) = g(2, 2n, n) -- 1, 16, 729, 65536, 9765625, 2176782336, 678223072849, 281474976710656, 150094635296999121, 100000000000000000000, 81402749386839761113321, 79496847203390844133441536, 91733330193268616658399616009

googo: a(n) = g(2, n, 2n) -- 2, 16, 216, 4096, 100000, 2985984, 105413504, 4294967296, 198359290368, 10240000000000, 584318301411328, 36520347436056576, 2481152873203736576, 182059119829942534144, 14348907000000000000000

googoo: a(n) = g(3, 2, 2n) -- 1, 256, 16777216, 11112006825558016, 18446744073709551616, 39346408075296537575424,

104857600000000000000000000, 341427877364219557396646723584,

1333735776850284124449081472843776, 6156119580207157310796674288400203776,

33145523113253374862572728253364605812736, 205891132094649000000000000000000000000000000

happy couple: referring to integers, f(2n - 1) = Sg(2, 2, d(2n - 1)) and f(2n) = Sg(2, 2, d(2n)) -- 31, 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

*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

h-ban:not containing an "h" -- 0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 25, 26, 27, 29, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 90, 91, 92, 94, 95, 96, 97, 99, 101, 102, 104,

heptagonal gnomic: A016861 ending in one or six, a(n) = n(5n - 3)/2 - (n - 1)(5(n - 1) - 3)/2 = 5n + 1 -- 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231

hex: A003215 a(n) = 3n(n + 1) + 1

h-ish: containing an "h" -- 3, 8, 13, 18, 23, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 48, 53, 58, 63, 68, 73, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 93, 98, 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, 128, 129, 130

Horner: [Jack Horner's pulling out of pi] A032445 number of digits to reach n in decimal expansion of p -- 2, 7, 1, 3, 5, 8, 14, 12, 6, 50, 95, 149, 111, 3, 5, 40, 96, 426, 37, 54, 94, 137, 18, 293, 91, 8, 30, 26, 199, 67, 140

i-ban: not containing an "i" -- 0, 1, 2, 3, 4, 7, 10, 11, 12, 14, 15, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 79, 100, 101, 102, 103, 104, 107, 110, 11, 112, 114, 117, 120, 122, 123, 124, 127, 140, 141, 142, 143, 144, 147, 170, 171, 172, 173, 174, 177, 200, 201, 202, 203, 204, 207, 210, 211, 212, 213, 214, 217,

*icosahedral gnomic: A093500 a(n) = n(5g(2, 2, n) - 5n + 2)/2 - (n - 1)(5g(2, 2, n - 1) - 5(n - 1) + 2)

i-ish: containing an "i" -- 5, 6, 8, 9, 13, 16, 18, 19, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 105, 106, 108, 109, 113, 1176, 118, 119, 125, 126, 128,

immodest: referring to integers not modest, n = N[n/g(2, a, 10)] (mod (n - [n/g(2, a, 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 = NS(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

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:?] A079721 referring to average of two consecutive emirps

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

intwo: number with 2 interiorly, a(n) = a[g(2, [log(b + 2), 10] + b[log(c + 1)] + c -- 120, 121, 123, 124, 125, 126, 127, 128, 129, 320, 321, 323, 324, 325, 326, 327, 328, 329, 420, 421, 423, 424, 425, 426, 427, 428, 429, 520, 521, 523

Ir-ish: containing "ir" -- 13, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,

Langford, modified: referring to integers with n digits between digits n including 0 and other single digits -- 0, 101, 2002, 31013, 20121, 12102, 23123, 312132, 23421314, 41312432, 2302131, 1312032

*left primorial: A079096 sum of factorials of all prime less than n, #n = (n - 1)# + #(n - 2)

lil: [lucky-indexed-lucky] 1, 7, 11, 29, 199, 5778, 1149851

lime: [sublime backformation] number n such that (n - 1)! < e(A81357 - ½) < n! where A81357 = sublime -- 4, 58, ?

L-ish: containing an "l" -- 11, 12, 111, 112, 211, 212, 311, 312, 411, 412, 511, 512, 611, 612, 711, 712, 811, 812, 911, 912, 1011, 1012, 1111, 1112, 1211, 1212, 1311, 1312, 1411, 1412, 1511, 1512, 1611, 1612, 1711, 1712, 1811, 1812, 1911, 1912, 2011, 2012, 2111, 2112, 2211, 2212, 2211, 2212, 2311, 2312, 2411, 2412, 2511, 2512,

*live: [prime:emirp::evil:?] A091017 non-palindromic integer which has an even number of ones in binary and whose reverse does too

magic: a(n) = g(99, n, n, n, n - 1, n, n) -- 1, 4, g(99, 3, 3, 3, 2, 3, 3), g(99, 4, 4, 4, 3, 4, 4)

Malu: [prime:emirp:Ulam:?] 1, 2, 3, 4, 6, 8, 11, 26, 28, 62, 77, 82, 99,

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: referring to integer with all three of 4, 5 or 6 -- 456, 465, 546, 564, 645, 4654, 4456, 4465, 4546, 4564, 4645, 4654, 5456, 5465, 5546, 5564, 5645, 5654, 6456, 6465, 6546, 6564, 6645, 6654

m-ish: containing an "m" -- 1000000, 1000001, 1000003, 1000004, 1000005, 1000006, 1000007, 1000008, 1000009, 1000010, 1000011, ...

*more-or-less prime: A045718 f(2n) = p(n) - 1, f(2n - 1) = p(n) + 1

*mostly evil: [prime:mostly prime::evil:?] A093505 a(n) = [A1969/2 + ½]

mostly-harmless: without three-fourths of a, h, m or r -- 0, 4, 8, 14, 18, 24, 28, 40, 41, 42, 45, 46, 47, 49, 54, 58, 64,68, 74, 78, 80, 81,82, 85, 86, 87, 89, 94, 98, 1000000, 1000001, 1000005, 1000006, 1000007,1000009, 1000010, 1000011, 1000012, 1000015, 1000016, 1000017, 1000019, 1000020, 1000021, 1000022, 1000025, 1000026, 1000027, 1000029, 1000050, 1000051, 1000052, 1000055, 1000056, 1000057, 1000059, 1000060

*mostly-ugly:

mostly-useless: without two-thirds of e, s or u -- 0, 1, 3, 4, 6, 8, 9, 10, 11, 12, 13, 15, 18, 19

multiplicadditive: alternately multiplying by and then adding, a(n) = ((n - 3) + (n - 2))*(n - 1), if n = 0 (mod 2), a(n) = (n - 3)*(n - 2) + (n - 1), if n = 1 (mod 2) -- 1, 1, 2, 4, 6, 18, 21, 84, 88, 440, 445, 2670, 2676, 18732, 18739, 149912, 149920, 1349280, 1349289, 13492890, 13492900, 148421900, 148421911, 1781062932, 1781062944, 2315381272, 23153818285, 324153455990, 324153456004, 4862301840060, 4862301840075, 77796829441200, 77796829441216, 1322546100500670, 1322546100500690

*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 ...."

neve: [prime:emirp::even:?] A79720 a(n) = 2a, R(a(n)) = 2b, 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

nonacci: A104144 Fibonacci-like sequence but adding previous 9 numbers, a(n) = a(n - 1) + a(n - 2) + a(n - 3) + a(n - 4) + a(n - 5) + a(n - 6) + a(n - 7) + a(n - 8) + a(n - 9)

Nosnora: [Aronson ananym] Aronson number whose reverse is also -- 1, 4, 11, 61, 42, 92, 33, 53, 93, 54, 74, 15, 65, 85, 26, 46, 96, 37, 87, 8, 48, 98, 49, 99, 401, 111, 611, 221, 621, 131, 631, 241, 741, 851, 461, 961, 471, 181, 381, 391, 991, 502, 802, 412, 22, 622, 132, 732, 342, 942, 452, 72, 882, 303, 703, 913, 323

*nth n in pi: A101196

*number name as if base 36: A072922 referring to integer resulting from interpreting English name as if in base 36

*number name as if base 27: A072959 referring to integer resulting from interpreting English name as if in Sallows' base 27

*oban:, A008521 not containing an "o"

*octonacci: A079262 referring to integers formed like Fibonacci numbers, but by adding previous 8, a(n) = a(n - 1) + a(n - 2) + a(n - 3) + a(n - 4) + a(n - 5) + a(n - 6) + a(n - 7) + a(n - 8)

odious: A000069 with odd number of ones in binary

OEIS: [on-line encyclopedia of integer sequences] A91967, a(n) = An(n), nth term in nth sequence -- 1, 2, 1, 0, 2, 3, 0, 6, 6, 4, 44, 1, 180, 42, 16, 1096, 7652, 13781, 8, 24000, 119779, 458561, 152116956851941670912

pabelian: [palindromic abelian] 1, 2, 3, 4, 5, 7, 9, 11, 33, 77, 99, 101

pansquare: [g(2, 2, pancake - cake)] a(n) =g(2, 2, (1 + n(n + 1)/2 - (g(2, 3, n) + 5n + 6)/6) -- 0, 1, 16, 400, 3136, 48400, 132496, 665856, 1299600, 4096576, 16483600, 24601600, 71166096, 131790400, 175403536, 615238416, 1171008400, 1430352400, 2511613456, 4202150976, 6750265600, 9079040656, 13801550400, 23133193216, 29480890000, 33161866816, 41679672336, 46578272400, 57822935296, 116537573376

peban: [palindromic eban] 2, 4, 6, 44, 66, 2002, 4004, 6006, 40004, 44044, 60006, 64064, 66066, 2000002, 2002002, 2004002, 2006002, 4000004

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] a(n) = R(n) -- 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

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,

phex: [palindromic hex] 1, 7, 919, 1081801, 1188811, 1946491

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

Phickover: [pi:phi:Pickover:?] decimal place of first n digits of e in phi -- 20, 65, 1463, 17125

plucky: [palindromic lucky] 1, 3, 7, 9, 33, 99, 111, 141, 151, 171, 303

poctal: [palindromic octal] referring to integer without 8 or 9, such that x = n (base 8), such that n = R(n) -- 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

*poddish: [palindromic oddish] A092361 a(n) = ag(2, [g(2, [log(c)] + 1, 10)(2b - 1) + c, 10], 10) + g(2, [log(c)] + 1, 10)(2b - 1) + c = R(a(n))

podious: [palindromic odioius] n = R(A69) -- 1, 2, 4, 7, 8, 11, 22, 44, 55, 88

powertrain [Conway] n = abcdef..., a(n) = a^b*c^d...

pring: [palindromic ring] a(n) = (n - 1)(2a(n - 1) + 3a(n - 2))/(n + 1) = R(n) -- 0, 1, 3, 6, 232

Proman: [palindromic Roman] 1, 2, 3, 5, 10, 19, 20, 30, 50, 100, 190, 200, 300, 500, 1000, 1900, 2000, 3000, 5000, 10000, 19000, 20000, 30000, 50000, 100000, 190000, 200000, 300000, 500000, 1000000, 2000000, 3000000, 5000000, 10000000, 19000000, 20000000, 30000000, 50000000, 100000000

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

ptriangular: [palindromic triangular] 1, 3, 6, 55, 66, 171, 595, 666, 3003, 5995

quadraprime: [prime:biprime::composite:?] referring to composite with at least four prime factors which may or may not be different, a(n) = p(n')*p(n")*p(n"')*p(n"") -- 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

quarter-cube: [square:quarter-square::cube:?] a(n) = [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

Rakerpak: [Kaprekar ananym] referring to integer n such that n = a + b = R(n) and g(2, 2, n) = a10c + b, for some c = 1, a = 0 and 0 = b < g(2, n, 10) , with n! = g(2, a, 10), f(1) = 1 -- 1, 9, 55, 99, 999, 7777, 9999, 22222, 99999,

r-ish: containing an "r" -- 3, 4, 13, 14, 23, 24, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 53, 54, 63, 64, 73, 74, 83, 84, 93, 94, 103, 104, 113, 114, 123, 124, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 153, 154, 163, 164, 173, 174, 183, 184, 193, 194, 203

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

*Roman numeral as base-36: A073421 referring to integer transformed to Roman numeral then interpreted as if in base 36

*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."

satyr: [sort-add-then-you-reverse] a(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

selfish: [9:9-ish::self:?] contains a self-number string not of the form b + Sd(b)), a(n) = ag(2, [g(2, [log(c)] + 1, 10)N(b + Sd(b)) + c, 10], 10) + g(2, [log(c)] + 1, 10)N(b + Sd(b)) + c -- 1, 3, 5, 7, 9, 10, 11, 12, 13, 15, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 105, 107, 109, 110, 111, 112, 113, 115, 117, 119, 121, 123, 125, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 143, 145, 147, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 163, 165,167, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 183, 185, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209

selfless: referring to integers, a(n) = N(x + S(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

*semi-Tribonacci: [Fibonacci:semi-Fibonacci::Tribonacci:?] A074364 f(0) = 0, f(1) = 1; f(2x) = f(x), f(2x + 1) = f(2x) + f(2x - 1) + f(2n - 2)

*s-inner: A072887 referring to integer not s-ain't

*slices of pi: A016062 digital expansion of pi such that a(n) > a(n -1)

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

*spiro-Tribonacci: A092360 a(n) = a(n - 1) + f(a) + f(b), such that f(a) and f(b) are nearest when terms are arranged in a spiral. In the case of a tie in nearness, the chronologically nearer value is used.

*spiro-Tetronacci: A092369 a(n) = a(n - 1) + f(a) + f(b) + f(c), such that f(a), f(b) and f(c) are nearest when terms arranged in a spiral. In the case of a tie in nearness, the chronologically nearer value is used.

Squaran: [cube:Cuban::square:?] a(n) = (p - 1)/2 -- 1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 26, 29, 30, 33, 36, 39, 41, 44, 48, 50, 51, 53, 54, 56, 63, 65, 68, 69, 74, 75, 78, 81, 83, 86, 89, 90, 95, 96, 105, 111, 113, 114, 116, 119, 120, 125, 128, 131, 134, 135

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,

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 + ½] -- 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::minimal:?] A79717 -- 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 + ½]

subsquare: a(n) = [g(2, 2/e, n) + ½] -- 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

subulysses: [factorial:subfactorial::Ulysses:?] 0, 6, 2.805300541375g(2, 12, 10), > 4.932456888g(2, 153, 10)

*suburban: A072955 referring to integer without b, r, s or u

supercake: [factorial:superfactorial::cake:?] referring to the product of previous cake integers, a(n) = P((g(2, 3, n) + 5n + 6)/6) -- 1, 2, 8, 64, 960, 24960, 1048320, 67092480, 6239600640, 811148083200, 142762062643200, 3140765378150400, 939088848066969600

supercats: [factorial:superfactorial:CATS:?] 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, a(n) = Pg(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:?] a(n) = P(2n) -- 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200, 81749606400, 1961990553600, 51011754393600, 142832913020800

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::Jacobsthal-Lucas:?] 1, 5, 35, 595, 18445, 1198925, 152263475, 39131713075, 19996305381325

superkolakoski: [a(n) = A2a(n - 1) -- 1, 2, 4, 4, 4, 8, 8, 16, 32, 32, 64, 128, 128, 128, 256, 256, 256, 512, 1024, 1024, 2048, 2048, 2048, 4096, 4096, 8192, 16384, 16384, 16384, 32768, 32768, 32768, 65536, 65536,

superménage: [factorial:superfactorial:: ménage:?] referring to product of previous non-nero menage integers -- 3, 39, 3237, 1916304, 9238501584, 406300061162736, 180646289093747539968

supermersenne: [factorial:superfactorial::Mersenne:?] referring to product of previous Mersenne integers, a(n) = PM(i) = Pg(2, p(i), 2) - 1) -- 3, 21, 651, 82677, 169239819, 1386243357429, 181696303101576448

super-1: [3:1::super-3:?] n such that 2n contains "1" -- 5, 6, 7, 8, 9, 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, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 105, 106, 107, 108, 109, 500, 501, 502, 503, 504, 505, 506, 507, 508

super-2: [3:2::super-3:?] n such that 2g(2, 2, n) contains "22" -- 19, 31, 69, 81, 105, 106, 107, 119, 127, 131, 169, 181, 190, 231, 247, 269, 281,

superpancake: [factorial:superfactorial::pancake:?] referring to product of previous pancake integers, a(n) = (n(n + 1)/2 + 1)a(n - 1) -- 2, 8, 56, 616, 9856, 216832, 6288128, 232660736, 10702393856, 599334055936, 40155381747712, 3172275158069250, 291849314542370816

superpodd: [factorial:superfactorial::podd:?] a(n) = P(2n + 1) = P(R(2n + 1)) -- 1, 3, 15, 105, 945, 10395, 343035, 18866925, 1452753225, 143822569275, 14526079496775, 1612394824142020

superprimorial: A006939 aka Chernoff referring to product of first n primorials, a(n) = ns# = n#(n - 1)s# -- 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, a(n) = g(2, 2, n)a(n - 1) = g(2, 2, n!) -- 1, 4, 36, 576, 14400, 518400, 25401600, 1625702400, 131681894400, 13168189440000, 1593350922240000, 220442532802560000, 38775788043632640000, 7600054456551997440000

superstar: a(n) = Pi(3i - 2) -- 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000

supervampire: [factorial:superfactorial::vampire:?] referring to product of previous vampire integers -- 126, 19278, 13263264, 15995496384, 20074347961920, 25293678432019200, 35284681412666785792

*taliban: [a:tali::aban:?] A072954 referring to integer without a, i, l or t

*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."

tetrational factorial: a(n) = g(3, a(n - 1), n) -- 1, 2, 9, g(3, 9, 4) > g(2, 153, g(3, 5, 10))

toscodicity: A072420 minimum number of steps needed to transform the integer into 153 by the triple-or-sum-of-cube-of-digits (TOSCOD) operator, a(n) -- 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

*triple-digit inflation: digital expansion in which f(d(n)) = 3d(n) -- 1, 3, 9, 27, 621, 1863, 324189, 961232427, 2718369612621, 6213249182718361863, 1863961227324621324918324189, 3241862718366219612186361227324961232427, 9612324186213249181863271836324189183662196122718369612621

*turban: A072956 without letters r, t, or u

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

uglier: number divisible only by 6, 10, or 15 a(n) = 0 (mod 6, mod 10 or mod 15) -- 6, 10, 12, 15, 18, 20, 24, 30. 36, 40, 45, 48, 50, 54, 60, 70,72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 174, 180, 186

ugliest: a(n) = 60n -- 30, 60, 90, 120, 180, 240, 270, 300, 360, 420, 450, 480, 540, 600, 720, 750, 810, 900, 960, 1080, 1200, 1260, 1350

ugly: A0512037 aka Hamming, with prime divisors > 5

uple: [nonuple backformation] a(n) N= 0 (mod 9) -- 0, 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 70, 71, 73, 74, 75, 76

*urban: A072957 referring to integer without r or u

*useless: A073418 referring to integer without e, s or u

vampirish: numbers with a vampire string -- 126, 153, 688, 1126, 1153, 1206, 1255, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 1395, 1435, 1503, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 1688, 1827, 2126, 2153, 2187, 2688, 3126, 3153, 3159, 3688, 3784, 4126, 4153, 4688, 5126, 5153, 5688, 6126, 6153, 6688, 6880, 6881, 6882, 6883, 6884, 6885, 6886, 6887, 6888, 6889, 7126, 7153, 7688

v-ish: containing a "v" -- 5, 7, 11, 12, 25, 27, 35, 37, 45, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 87, 95, 97, 105, 107, 111, 112, 125, 127, 135, 137, 145, 147, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 165, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 185, 187, 195, 197, 205

*worthless: A073419 referring to integer without h, o, r, t, or w -- 5, 6, 7, 9, 11, 55555 (read as five fives)

ylgu: [prime:emirp::ugly:?] number divisible by only by 2, 3 or 5, whose reverse is also a(n) = 0 (mod 2, mod 3, or mod 5) and R(a(n) = 0 (mod 2, mod 3, or mod 5) -- 1, 2, 3, 4, 5, 6, 8, 9, 10, 20, 27, 30,40, 45, 50, 54, 60, 72, 80, 81, 90,100, 108,

neckendorp expansion: A93712 [Fibonacci:prime:neckendorf:?] a(n) = n written abbreviatedly as strings of decreasing primes -- 1, 2, 3, 31, 5, 51, 7, 71, 72, 73, 11, 111, 13, 131, 132, 133, 17, 171, 19, 191, 192, 193, 23, 231, 232, 233, 2331, 235, 29, 291, 31, 311, 312, 313, 3131, 315, 37, 371, 372, 373, 41, 411, 43, 431, 432, 433, 47, 471, 472, 473, 4731, 475, 53, 531, 532, 533, 5331, 535, 59, 591, 61, 611, 612, 613, 6131, 615, 6151, 617, 6171, 6172, 71