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.

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] https://oeis.org/A104144 integer not nonacci, f(n) = N(f(n - 1) + f(n - 2) + f(n - 3) + f(n - 4) + f(z - 5) + f(z - 6) + f(z - 7) + f(z - 8) + f(z - 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(z) = N(z(7z - 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 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: A79718 digital expansion of perfect numbers -- 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: A72763 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-numberdrome, odd-digited: A93472, 159, 258, 357, 456, 555, 654, 753, 852, 951, 11599, 12589, 13579, 14569, 15559, 16549, 17539, 18529, 19519, 21598, 22588, 23578, 24568, 25558, 26548, 27538, 28528, 29518, 31597, 32587, 33577, 34567, 35557, 36547, 37537, 38527, 39517, 41596, 42586, 43576, 44566, 45556, 46546, 47536

Babylonian reciprocal: ["igibum"] A94086 number which when multiplied by zth ugly number gives a power of sixty, f(z) = g(2, [log(z)/log(60)], 60)/A51037(z) -- 60, 30, 20, 15, 12, 10, 450, 400, 6, 5, 4, 225, 200, 3, 150, 144, 8000, 2, 6750, 100, 90, 80, 75, 72, 4000, 1, 3375, 50, 48, 45, 160000, 40, 2250, 36, 2000, 30, 1728, 101250, 1600, 25, 24, 1350, 80000, 20, 1125, 18, 1000, 16, 15, 3200000, 864, 50625, 800, 750, 12, 675, 40000, 10, 576, 33750, 9, 32000

Bantu: [ban two] A52404 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

basic: inventory of z in all bases z 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

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, f(z) = [g(2, (3z + 3)(p -3), 10] - [g(2, 3z, 10)(p - 3)] -- 141, 592, 653, 589, 793, 238, 462, 643

binary reversal: f(z) = y (base 2) = R(y) (base 2) -- 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 zero f(z) = #(d(z) = 0)g(2, d(n\z), 10), 10 + #(d(z) = 1)g(2, (d(z) - 1), 10) + ... + #(d(z) = 9) -- 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(z) = 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

bipolar: with only minimum and maximum digits, f(z) = 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:?] A72958 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

cancrine: A81365 word-palindrome number -- 101, 202, 303, 404, 505, 606, 707, 808, 909, 1001, 2002, 3003, 4004, 5005, 6006, 7007, 8008, 9009, 10010, 110011, 120012, 130013,

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, modified: A72761 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

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:?] A81367 referring to integer divisible by a prime cubed, f(z) = 0 (mod g(2, 3, p) -- 8, 16, 27, 32, 64, 81, 125, 128, 216, 243, 256, 343, 432, 512, 625, 648, 729, 864, 1000, 1024, 1296, 1331, 1728, 1944, 2000, 2048, 2187, 2197, 2401, 2592, 2744, 3125, 3375, 3456, 3888, 4000, 4096, 4913, 5000, 5184, 5488, 5832, 6561, 6859, 6912, 7776, 8000,

cubic gnomic: 7, 19, 37, 61

curvaceous: A72960 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: A72961 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, ..., 2[g(2, 101, 10)/9] + 3

d-ban: not containing a "d" -- 0, 1, 2, 3, 4, 5, 6, 7, 8, ..., 99, 1000000, 1000001, ...

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,

dearest: 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: Fibonacci-like sequence but adding previous 10, f(z) = f(z - 1) + f(z - 2) + f(z - 3) + f(z - 4) + f(z - 5) + f(z - 6) + f(z - 7) + f(z - 8) + f(z - 9) + f(z - 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

decinary reversal: A93474 alternating between base 2 and base 10 reversing between f(z + 1) = R(f(z)(base 2)) (base 10) -- 0, 1, 1, 3, 1, 5, 3, 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, 113, 9, 73, 41, 105, 25, 89

DENEAT: A73053 referring to integer generated by application of DENEAT (digits-even-not-even-and-total) operator, f(z) = 100(#(d(x))) + 10(#(d(y)) + #(d(z)) where d(x) = 0 (mod 2) and d(y) = 1 (mod 2) -- 2n11, 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: A73054 referring to number of applications of DENEAT (digits-even-not-even-and-total) operator needed to reduce z to 123, f(z) = #(DENEAT(z)) -- 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

Diephi: A93473 [Diep + phi] next z digits of phi -- 1, 61, 803, 3988, 74989, 484820, 4586834, 36563811, 772030917, 9805762862, 13544862270, 526046281890, 2449707207204, 18939113748475, 408807538689175, 2126633862223536, 93179318006076672, 635443338908659593, 9582905638322661319, 92829026788067520876, 689250171169620703222, 1043216269548626296313,

61443814975870122034080, 588795445474924618569536,

4864449241044320771344947

digital power: [addition:exponentiation::digital sum:?] A75877 f(z) = Pd(i), g(2, d(i + 1), where z = 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:?] A7954 f(z) = P(d(i)), where z = 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,

Diglnow: [alphadigital  Dowling] 1, 2, 13, 413, 8512, 57632, 547732, 9996320, 554733220, 5449917320, 855444999177333220

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

dodecahedral gnomic: A93485 f(z) = z(3z - 1)(3z -2)/2 - (z - 1)(3(z -1) -1)(3(z - 1) - 2)/2 = -- 19, 64, 136, 235, 361, 514, 694, 901, 1135, 1396, 1684, 1999, 2341, 2710, 3106, 3529, 3979, 4456, 4960, 5491, 6049, 6634, 7246, 7885, 8551, 9244, 9964, 10711, 11485, 12286, 13114, 13969, 14851, 15760, 16696, 17659, 18649, 19666, 20710, 21781, 22879, 24004, 25156, 26335, 27541

double-header: integer with first two digits identical, f(z) = 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:?] A79078 n## = p(i)p(i - 2)##; ((2n)## = P(p(2i)) and (2n + 1)## = P(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

dufactorial: f(z) = (z!)!  -- 1, 2, 720, 620448401733239439360000, 668950291344912705758811805409037258675274633313802981029567135230

163355724496298936687416527198498130815763789321409055253440858940

812185989848111438965000596496052125696000000000000000000000000000

0

Eckover: A93648 [pi:e::Pickover:?] decimal place of first z 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,

exponential primorial: f(z) = g(p(z - 1), (2, 0), -1, p(z)) -- 1, 2, 9, 1953125, 1.286479g(2, 1.650582g(2, 6, 10)

faketorial: f(f(z)) = (z!)! -- 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: A73417 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

four-is: A72425 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

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

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

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

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

104857600000000000000000000, 341427877364219557396646723584,

1333735776850284124449081472843776, 6156119580207157310796674288400203776,

33145523113253374862572728253364605812736, 205891132094649000000000000000000000000000000

happy couple: referring to integers, f(2z - 1) = Sg(2, 2, d(2z - 1)) and f(2z) = Sg(2, 2, d(2z)) -- 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: A73416 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: A16861 f(z) = z(5z - 3)/2 - (z - 1)(5(z - 1) - 3)/2 = 5z + 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

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] A32445 number of digits to reach z 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: A93500 f(z) = z(5g(2, 2, z) - 5z + 2)/2 -(z - 1)(5g(2, 2, z - 1) - 5(z - 1) + 2) = -- 11, 36, 76, 131, 201, 286, 386, 501, 631, 776, 936, 1111, 1301, 1506, 1726, 1961, 2211, 2476, 2756, 3051, 3361, 3686, 4026, 4381, 4751, 5136, 5536, 5951, 6381, 6826, 7286, 7761, 8251, 8756, 9276, 9811, 10361, 10926, 11506, 12101, 12711, 13336, 13976, 14631, 15301, 15986

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, z = N[z/g(2, a, 10)] (mod (z - [z/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, z = NS(div(z)) -- 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:?] A79721 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

intwo: number with 2 interiorly, f(z) = 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, 113, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 213

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

left primorial: A79096 sum of factorials of all prime less than z, #z = (z - 1)# + #(z - 2) -- 1, 3, 9, 39, 249, 2559, 5559, 516069, 10215759, 233308629, 6703001859, 207263491989, 7628001626799, 311878265154009, 13394639596824039, 628284422185315449, 33217442899375360179, 1955977793053587999249

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

lime: [sublime backformation] number z such that (z - 1)! < e(A81357 - ½) < z! 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:?] A91017, non-palindromic integer which has an even number of ones in binary and whose reverse does too -- 15, 17, 27, 29, 30, 34, 36, 43, 45, 51, 54, 57, 58, 60, 63, 68, 71, 72, 75, 85, 86, 90, 92, 102, 108,113, 114, 126, 129,132, 135, 139, 144, 147, 150, 159,165,170, 175,177, 192, 195, 197, 198, 201, 204, 210, 216, 219, 226

magic: f(z) = g(99, z, z, z, z - 1, z, z) -- 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: A45718 f(2z) = p(z) - 1, f(2z - 1) = p(z) + 1 -- 1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 30, 32, 36, 38, 40, 42, 44, 46, 48, 52, 54, 58, 60, 62, 66, 68, 70, 72, 74, 78, 80, 82, 84, 88, 90, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 126, 128, 130, 132, 136, 138, 140, 148, 150, 152, 156, 158, 162, 164, 166, 168, 172, 174, 178, 180, 182, 190, 192,194, 196, 198, 200, 210, 212, 222, 224, 226, 228, 230, 232, 234, 238, 340

mostly evil: A93505 [prime:mostly prime::evil:?] :f(z) = [A1969/2 + ½] -- 0, 2, 3, 3, 5, 5, 6, 8, 8, 9, 10, 12, 12, 14, 15, 15, 17, 17, 18, 20, 20, 22, 23, 23, 24, 26, 27, 27, 26, 26, 30, 32, 33, 33, 34, 36, 36, 38, 39, 39, 40, 42, 43, 43, 45, 45, 46, 48, 48, 50, 51, 51, 53, 53, 54, 56, 57, 57, 58, 60, 60, 62, 63, 63, 65

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 prime: A81385 f(z) = [p/2 + ½] -- 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 16, 17, 18, 19, 20, 26, 27, 28, 29, 30, 36, 37, 38, 39, 40, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65

*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, f(z) = ((z - 3) + (z - 2))*(z - 1), if z = 0 (mod 2), f(z) = (z - 3)*(z - 2) + (z - 1), if z = 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: A72422 -- 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, 27, 53, 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:?] A79720 f(z) = 2a, R(f(z)) = 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, f(z) = f(z - 1) + f(z - 2) + f(z - 3) + f(z - 4) + f(z - 5) + f(z - 6) + f(z - 7) + f(z - 8) + f(z - 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

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

number name as if base 36: A72922 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

number name as if base 27: A72959 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

oban: A8521, not containing an "o" -- 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 50, 53, 55, 56, 57, 58, 59, 60, 63, 65, 66, 67, 68, 69, 70, 73, 75, 76, 77, 78, 79, 80, 83, 85, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98, 99, 300, 303, 305, 306, 307

octonacci: A79262 referring to integers formed like Fibonacci numbers, but by adding previous 8, f(z) = f(z - 1) + f(z - 2) + f(z - 3) + f(z - 4) + f(z - 5) + f(z - 6) + f(z - 7) + f(z - 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

OEIS: [on-line encyclopedia of integer sequences] A91967, f(z) = Az(z), zth term in zth 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)] f(z) =g(2, 2, (1 + z(z + 1)/2 - (g(2, 3, z) + 5z + 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] F(z) = R(z) -- 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 z 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: A92361 [palindromic oddish] f(z) = ag(2, [g(2, [log(c)] + 1, 10)(2b - 1) + c, 10], 10) + g(2, [log(c)] + 1, 10)(2b - 1) + c = R(f(z)) -- 1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 232, 252, 272, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 414, 434, 454, 474, 494, 505, 515, 525, 535, 545, 555, 575, 595, 616, 636, 656, 676, 696, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 818, 838, 858, 878, 898, 909

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

pring: [palindromic ring] f(z) = (z - 1)(2f(z - 1) + 3f(z - 2))/(z + 1) = R(z) -- 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

quarter-cube: [square:quarter-square::cube:?] f(z) = [g(2, 3, z)/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 z such that z = a + b = R(z) and g(2, 2, z) = a10c + b, for some c = 1, a = 0 and 0 = b < g(2, z, 10) , with z! = 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: A73427 -- 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: A73421 -- 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

s-ain't: A72886 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

satyr: [sort-add-then-you-reverse] f(z) = R(sort(z) + z) -- 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)), f(z) = 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, f(z) = 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:?] A74364 f(0) = 0, f(1) = 1; f(2x) = f(x), 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: A72887 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: A16062 -- digital expansion of pi such that f(z) > f(z -1) -- 3, 14, 15, 92, 653, 5897, 9323, 84626, 433832, 795028, 841971, 6939937, 51058209, 74944592, 307816406, 2862089986, 28034825342, 1170679821480, 8651328230664, 70938446095505, 82231725359408, 128481117450284, 1027019385211055

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: A92360, f(z) = f(z - 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. -- 0, 1, 1, 3, 5, 8, 13, 14, 28, 43, 45, 89, 135, 138, 143, 284, 430, 438, 451, 897,1356, 1404, 1446, 2878, 4352, 4423, 4511, 4645, 9245, 13979, 14203, 14476, 14757, 15184, 30225, 45693, 46407, 47275, 48164, 49512, 98573, 148982, 151235, 153968, 156749, 159599, 163923, 326400, 493201, 500431, 509206, 518140, 527296, 541186, 1077727, 1628158, 1651382, 1679564, 1708243, 1737476, 1767417, 1812826, 3610468, 5453519

spiro-Tetronacci: A92369, f(z) = f(z - 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. -- 0, 1, 1, 1, 3, 5, 9, 15, 25, 41, 68, 111, 181, 294, 299, 597, 900, 1505, 1522, 3041, 4577, 7642, 7691, 7772, 15529, 23367, 39005, 39225, 39585, 79102, 118979, 198556, 199330, 200520, 202316, 404333, 608146, 1013976, 1017903, 1023971, 1033111, 2064700, 3105429, 5177747, 5197657, 5220762, 5251754, 5298422, 10589072, 15926390, 26577834, 26679431, 26797246, 26955158, 27192824, 543446063, 81736968

Squaran: [cube:Cuban::square:?] f(z) = (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, z)/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:?] A79266 [z#/e + ½] -- 0, 1, 2, 11, 77, 850, 11047, 187806, 3568317, 82071280, 2380067130, 73782081030, 2729936998040, 111927416922654, 4812878927674130

subsquare: f(z) = [g(2, 2/e, z) + 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: A72955 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

supercake: [factorial:superfactorial::cake:?] referring to the product of previous cake integers, f(n) = P((g(2, 3, z) + 5z + 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, f(z) = Pg(2, 3, z) -- 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(z) = P(2z) -- 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: [f(z) = A2f(z - 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-zero menage integers -- 3, 39, 3237, 1916304, 9238501584, 406300061162736, 180646289093747539968

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

super-1: [3:1::super-3:?] z such that 2z 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:?] z such that 2g(2, 2, z) 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, f(z) = (z(z + 1)/2 + 1)f(z - 1) -- 2, 8, 56, 616, 9856, 216832, 6288128, 232660736, 10702393856, 599334055936, 40155381747712, 3172275158069250, 291849314542370816

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

superprimorial: A79264 referring to product of first z primorials, f(z) = zs# = z#(z - 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, f(z) = g(2, 2, z)f(z - 1) = g(2, 2, z!) -- 1, 4, 36, 576, 14400, 518400, 25401600, 1625702400, 131681894400, 13168189440000, 1593350922240000, 220442532802560000, 38775788043632640000, 7600054456551997440000

superstar: f(z) = 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:?] A72954 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

t-est: A72423 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

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

toscodicity: A72420 minimum number of steps needed to transform the integer into 153 by the triple-or-sum-of-cube-of-digits (TOSCOD) operator, f(z) -- 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(z)) = 3d(z) -- 1, 3, 9, 27, 621, 1863, 324189, 961232427, 2718369612621, 6213249182718361863, 1863961227324621324918324189, 3241862718366219612186361227324961232427, 9612324186213249181863271836324189183662196122718369612621

turban: A72956 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

uglier: number divisible only by 6, 10, or 15 f(z) = 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: f(z) = 60z -- 30, 60, 90, 120, 180, 240, 270, 300, 360, 420, 450, 480, 540, 600, 720, 750, 810, 900, 960, 1080, 1200, 1260, 1350

uple: [nonuple backformation] f(z) 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: A72957 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: A73418 -- 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

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: A73419 referring to integer without h, o, r, t, or w -- 5, 6, 7, 9, 11, 55555 (read as five fives), 66666, 77777, 99999, 555555, 666666, 777777, 999999, 5555555, 6666666, 7777777,9999999, 555555555, 666666666, 777777777, 999999999, 1111111111, 55555555555, 66666666666, 77777777777, 99999999999, 111111111111, 11111111111111, 111111111111111111, 1111111111111111111111,  5555555555555555555555555,

ylgu: [prime:emirp::ugly:?] number divisible by only by 2, 3 or 5, whose reverse is also f(z) = 0 (mod 2, mod 3, or mod 5) and R(f(z) = 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,

Zeckendorp expansion: A93712 [Fibonacci:prime:Zeckendorf:?] f(z) = z 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

zth z in pi: A101196 -- 1, 16, 17, 36, 48, 72, 96, 74, 55, 854, 709, 1080, 1076, 1636, 1657, 1651, 889, 1674, 1227, 2039, 1486, 2372, 2690, 2288, 2033, 2282, 1785, 2703, 4155, 3102, 3584, 3767, 4325, 3808, 3551, 4081, 3785, 3229, 4464, 4884, 4127, 4228, 5336, 3961, 4242, 3633, 4571, 3868, 4356, 5835