| A001235 |
Taxi-cab numbers: sums of 2 cubes in more than 1 way. |
1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656 |
|
| A303935 |
digit factorial chain length |
2, 1, 1, 16, 8, 10, 15, 32, 36, 35, 2, 2, 17, 33, 13, 10, 15, 32, 36, 35 |
S |
| A285361 |
The number of tight 3 X n pavings. |
1, 11, 64, 282, 1071, 1860, -5333, -44620, -105269, 177252, 2110491, 6035220, -4133909, -96953020, -330674501, -22641804, 4320755595, 17496163236, 11990343259, -185665997356 |
S |
| A244802 |
The 60º spoke (or ray) of a hexagonal spiral of Ulam. |
1, 10, 43, 100, 181, 286, 415, 568, 745, 946, 1171, 1420, 1693, 1990, 2311, 2656, 3025, 3418, 3835, 4276 |
S |
| A227919 |
Primes which remain prime when rightmost digit is removed. |
23, 29, 31, 37, 53, 59, 71, 73, 79, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 233 |
S |
| A214733 |
|
0, 1, -1, -2, 5, 1, -16, 13, 35, -74, -31, 253, -160, -599, 1079, 718, -3955, 1801, 10064, -15467 |
S |
| A167149 |
|
0, 1, 10000, 29997, 59992, 99985, 149976, 209965, 279952, 359937, 449920, 549901, 659880, 779857, 909832, 1049805, 1199776, 1359745, 1529712, 1709677 |
S |
| A164555 |
|
1, 1, 1, 0, -1, 0, 1, 0, -1, 0, 5, 0, -691, 0, 7, 0, -3617, 0, 43867, 0 |
S |
| A153893 |
a(n)=3*2^n-1 |
2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863 |
S |
| A152054 |
Bouncy numbers (numbers whose digits form a strictly non-monotonic sequence). |
101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151 |
S |
| A139566 |
Take sum of squares of digits of previous term, starting with 15 |
15, 26, 40, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16 |
S |
| A135519 |
a(n) = (14^n - 1)/13. |
1, 15, 211, 2955, 41371, 579195, 8108731, 113522235, 1589311291, 22250358075, 311505013051, 4361070182715, 61054982558011, 854769755812155, 11966776581370171, 167534872139182395 |
S |
| A135518 |
a(n) = (15^n - 1)/14. |
1, 16, 241, 3616, 54241, 813616, 12204241, 183063616, 2745954241, 41189313616, 617839704241, 9267595563616, 139013933454241, 2085209001813616, 31278135027204241, 469172025408063616 |
S |
| A134816 |
Padovan's spiral numbers. |
1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181 |
S |
| A134657 |
Numbers of the form p^2 + q^3 + r^4 with p, q and r primes. |
28, 33, 47, 49, 52, 68, 73, 92, 93, 98, 112, 114, 117, 133, 138, 145, 150, 157, 164, 166 |
S |
| A133500 |
The powertrain or power train map |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 |
S |
| A131865 |
a(n) = (16^n - 1)/15. |
1, 17, 273, 4369, 69905, 1118481, 17895697, 286331153, 4581298449, 73300775185, 1172812402961, 18764998447377, 300239975158033, 4803839602528529, 76861433640456465 |
S |
| A128834 |
Periodic sequence 0,1,1,0,-1,-1,... |
0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1 |
S |
| A122065 |
Take sum of squares of digits of previous term, starting with 74169 |
74169, 183, 74, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4 |
S |
| A121727 |
|
5, 13, 17, 25, 41, 29, 37, 61, 65, 85, 53, 113, 65, 101, 145, 73, 85, 89, 181, 145 |
S |
| A118905 |
|
7, 14, 17, 21, 23, 28, 31, 34, 35, 41, 42, 46, 47, 49, 51, 56, 62, 63, 68, 69 |
S |
| A107920 |
Lucas and Lehmer numbers with parameters (1+-sqrt(-7))/2. |
0, 1, 1, -1, -3, -1, 5, 7, -3, -17, -11, 23, 45, -1, -91, -89, 93, 271, 85, -457 |
S |
| A102859 |
Numbers that when squared and written backwards give a square again |
0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 26, 30, 31, 33, 99, 100, 101, 102, 103 |
S |
| A100959 |
Non-semiprimes. |
1, 2, 3, 5, 7, 8, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 27, 28, 29, 30 |
S |
| A098416 |
(A007529(n) + A098415(n)) / 4. |
|
S |
| A098415 |
Greatest members r of prime triples (p,q,r) with p<q<r=p+6. |
11, 13, 17, 19, 23, 43, 47, 73, 103, 107, 109, 113, 197, 199, 229, 233, 283, 313, 317, 353 |
S |
| A098414 |
|
7, 11, 13, 17, 19, 41, 43, 71, 101, 103, 107, 109, 193, 197, 227, 229, 281, 311, 313, 349 |
S |
| A098413 |
Middle members q of prime triples (p,q,r) with p<q<r=p+6. |
13, 19, 43, 73, 103, 109, 199, 229, 283, 313, 463, 619, 829, 859, 883, 1093, 1303, 1429, 1453, 1489 |
S |
| A098412 |
Greatest members p of prime triples (p, p+2, p+6). |
11, 17, 23, 47, 107, 113, 197, 233, 317, 353, 467, 647, 827, 863, 887, 1097, 1283, 1307, 1433, 1487 |
S |
| A091030 |
a(n) = (13^n - 1)/12. |
1, 14, 183, 2380, 30941, 402234, 5229043, 67977560, 883708281, 11488207654, 149346699503, 1941507093540, 25239592216021, 328114698808274, 4265491084507563, 55451384098598320, 720867993281778161 |
S |
| A090748 |
Numbers n such that 2^(n+1) - 1 is prime. |
1, 2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126, 520, 606, 1278, 2202 |
S |
| A089675 |
Numbers n such that 9*R_n - 2 is a prime number, where R_n = 11...1 (the repunit (A002275) of length n). Also numbers n such that 10^n - 3 is prime |
1, 2, 3, 17, 140, 990 |
S |
| A088002 |
Expansion of (1+x^2)/(1+x^2+x^5) |
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
S |
| A087204 |
Period 6: repeat [2, 1, -1, -2, -1, 1]. |
2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1 |
S |
| A086224 |
a(n)=7*2^n-1 |
6, 13, 27, 55, 111, 223, 447, 895, 1791, 3583, 7167, 14335, 28671, 57343, 114687, 229375, 458751, 917503, 1835007, 3670015 |
S |
| A082115 |
Fibonacci numbers modulo 3 |
0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2 |
S |
| A080709 |
Take sum of squares of digits of previous term, starting with 4 |
4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58 |
S |
| A079907 |
Numbers n such that 11*12^n-1 is prime |
1, 2, 21, 25, 33, 54, 78, 235 |
S |
| A079906 |
Numbers n such that 5*6^n-1 is prime |
1, 2, 6, 7, 11, 23, 33, 48, 68, 79, 116, 151, 205 |
S |
| A077800 |
|
3, 5, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109 |
S |
| A073649 |
Middle members of prime triples (p, p+4, p+6). |
11, 17, 41, 71, 101, 107, 197, 227, 281, 311, 461, 617, 827, 857, 881, 1091, 1301, 1427, 1451, 1487 |
S |
| A073648 |
Middle members of prime triples (p, p+2, p+6). |
7, 13, 19, 43, 103, 109, 193, 229, 313, 349, 463, 643, 823, 859, 883, 1093, 1279, 1303, 1429, 1483 |
S |
| A070635 |
a(n) = n mod (sum of digits of n). |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 4, 3, 2, 1, 0, 9, 0 |
S |
| A067500 |
Powers of 3 with digit sum also a power of 3. |
1, 3, 9, 27, 81, 243, 19683, 59049, 177147, 1594323, 43046721, 129140163, 10460353203, 7625597484987, 617673396283947, 50031545098999707, 150094635296999121 |
S |
| A065091 |
The odd prime numbers |
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73 |
S |
| A062569 |
a(n) = sigma(n!). |
1, 1, 3, 12, 60, 360, 2418, 19344, 159120, 1481040, 15334088, 184009056, 2217441408, 31044179712, 442487616480, 6686252969760, 107004539285280, 1926081707135040, 34683832925921088, 693676658518421760 |
S |
| A061909 |
Skinny numbers: numbers n such that there are no carries when n is squared by "long multiplication". |
0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 30, 31, 100, 101, 102, 103, 110, 111, 112 |
S |
| A061602 |
Sum of factorials of the digits of n |
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881 |
S |
| A061457 |
Numbers n such that n and its reversal are both squares. |
0, 1, 4, 9, 100, 121, 144, 169, 400, 441, 484, 676, 900, 961, 1089, 9801, 10000, 10201, 10404, 10609 |
S |
| A061006 |
|
0, 1, 2, 2, 4, 0, 6, 0, 0, 0, 10, 0, 12, 0, 0, 0, 16, 0, 18, 0 |
S |
| A060421 |
Numbers n such that the first n digits of the decimal expansion of Pi form a prime. |
1, 2, 6, 38 |
S |
| A060305 |
Period of Fibonacci numbers mod prime(n). |
3, 8, 20, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70 |
S |
| A057588 |
Kummer numbers: -1 + product of first n consecutive primes. |
1, 5, 29, 209, 2309, 30029, 510509, 9699689, 223092869, 6469693229, 200560490129, 7420738134809, 304250263527209, 13082761331670029, 614889782588491409 |
S |
| A057166 |
|
4, 8, 10, 12, 14, 16, 20, 22, 23, 25, 27, 29, 31, 35, 37, 38, 40, 42, 44, 46 |
S |
| A057165 |
|
1, 2, 3, 5, 6, 7, 9, 11, 13, 15, 17, 18, 19, 21, 24, 26, 28, 30, 32, 33 |
S |
| A056725 |
Numbers n such that 9*10^n-1 is prime |
1, 3, 7, 19, 29, 37, 93 |
S |
| A055932 |
Numbers where all prime divisors are consecutive primes starting at 2. |
1, 2, 4, 6, 8, 12, 16, 18, 24, 30, 32, 36, 48, 54, 60, 64, 72, 90, 96, 108 |
S |
| A055012 |
Sum of cubes of the digits of n written in base 10. |
0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1, 2, 9, 28, 65, 126, 217, 344, 513, 730 |
S |
| A054320 |
Expansion of g.f.: (1 + x)/(1 - 10*x + x^2). |
1, 11, 109, 1079, 10681, 105731, 1046629, 10360559, 102558961, 1015229051, 10049731549, 99482086439, 984771132841, 9748229241971, 96497521286869, 955226983626719, 9455772314980321, 93602496166176491, 926569189346784589 |
S |
| A051885 |
Smallest number whose sum of digits is n. |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199 |
S |
| A051876 |
|
0, 1, 24, 69, 136, 225, 336, 469, 624, 801, 1000, 1221, 1464, 1729, 2016, 2325, 2656, 3009, 3384, 3781 |
S |
| A051875 |
|
0, 1, 23, 66, 130, 215, 321, 448, 596, 765, 955, 1166, 1398, 1651, 1925, 2220, 2536, 2873, 3231, 3610 |
S |
| A051874 |
|
0, 1, 22, 63, 124, 205, 306, 427, 568, 729, 910, 1111, 1332, 1573, 1834, 2115, 2416, 2737, 3078, 3439 |
S |
| A051873 |
|
0, 1, 21, 60, 118, 195, 291, 406, 540, 693, 865, 1056, 1266, 1495, 1743, 2010, 2296, 2601, 2925, 3268 |
S |
| A051872 |
|
0, 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, 1417, 1652, 1905, 2176, 2465, 2772, 3097 |
S |
| A051871 |
|
0, 1, 19, 54, 106, 175, 261, 364, 484, 621, 775, 946, 1134, 1339, 1561, 1800, 2056, 2329, 2619, 2926 |
S |
| A051870 |
|
0, 1, 18, 51, 100, 165, 246, 343, 456, 585, 730, 891, 1068, 1261, 1470, 1695, 1936, 2193, 2466, 2755 |
S |
| A051869 |
|
0, 1, 17, 48, 94, 155, 231, 322, 428, 549, 685, 836, 1002, 1183, 1379, 1590, 1816, 2057, 2313, 2584 |
S |
| A051868 |
|
0, 1, 16, 45, 88, 145, 216, 301, 400, 513, 640, 781, 936, 1105, 1288, 1485, 1696, 1921, 2160, 2413 |
S |
| A051867 |
|
0, 1, 15, 42, 82, 135, 201, 280, 372, 477, 595, 726, 870, 1027, 1197, 1380, 1576, 1785, 2007, 2242 |
S |
| A051866 |
|
0, 1, 14, 39, 76, 125, 186, 259, 344, 441, 550, 671, 804, 949, 1106, 1275, 1456, 1649, 1854, 2071 |
S |
| A051865 |
|
0, 1, 13, 36, 70, 115, 171, 238, 316, 405, 505, 616, 738, 871, 1015, 1170, 1336, 1513, 1701, 1900 |
S |
| A051682 |
|
0, 1, 11, 30, 58, 95, 141, 196, 260, 333, 415, 506, 606, 715, 833, 960, 1096, 1241, 1395, 1558 |
S |
| A051626 |
Length of the period of decimal representation of 1/n, or 0 if 1/n terminates. |
0, 0, 1, 0, 0, 1, 6, 0, 1, 0, 2, 1, 6, 6, 1, 0, 16, 1, 18, 0 |
S |
| A051624 |
|
0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729 |
S |
| A051179 |
Sequence+-1 |
1, 3, 15, 255, 65535, 4294967295 |
S |
| A051005 |
prime values of PartitionsQ. |
2, 2, 3, 5, 89, 29927 |
S |
| A050935 |
a(1)=0, a(2)=0, a(3)=1, a(n+1) = a(n) - a(n-2). |
0, 0, 1, -1, 1, 0, -1, 2, -2, 1, 1, -3, 4, -3, 0, 4, -7, 7, -3, -4 |
S |
| A050523 |
Primes of the form 7*2^n-1 |
13, 223, 3583, 917503, 14680063, 3758096383, 246290604621823 |
S |
| A050278 |
|
1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, 1023457968, 1023457986, 1023458679, 1023458697, 1023458769, 1023458796, 1023458967, 1023458976, 1023459678, 1023459687 |
S |
| A048328 |
Numbers that are repdigits in base 3. |
0, 1, 2, 4, 8, 13, 26, 40, 80, 121, 242, 364, 728, 1093, 2186, 3280, 6560, 9841, 19682, 29524 |
S |
| A046867 |
Numbers n such that 10*11^n-1 is prime |
1, 3, 37, 119, 255, 355 |
S |
| A046866 |
Numbers n such that 6*7^n-1 is prime |
1, 2, 7, 18, 55, 69, 87, 119, 141, 189, 249, 354 |
S |
| A046865 |
Numbers n such that 4*5^n-1 is prime |
0, 1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339 |
S |
| A046132 |
Greater of cousin primes |
7, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353 |
S |
| A046124 |
|
23, 29, 59, 79, 269, 619, 659, 1109, 1499, 1619, 1759, 1879, 2389, 2689, 3319, 3929, 4019, 5119, 5399, 5449 |
S |
| A046123 |
|
17, 23, 53, 73, 263, 613, 653, 1103, 1493, 1613, 1753, 1873, 2383, 2683, 3313, 3923, 4013, 5113, 5393, 5443 |
S |
| A046122 |
|
11, 17, 47, 67, 257, 607, 647, 1097, 1487, 1607, 1747, 1867, 2377, 2677, 3307, 3917, 4007, 5107, 5387, 5437 |
S |
| A046120 |
|
19, 29, 43, 59, 79, 109, 113, 163, 179, 239, 269, 283, 359, 379, 569, 599, 619, 659, 739, 953 |
S |
| A046119 |
|
13, 23, 37, 53, 73, 103, 107, 157, 173, 233, 263, 277, 353, 373, 563, 593, 613, 653, 733, 947 |
S |
| A046118 |
|
7, 17, 31, 47, 67, 97, 101, 151, 167, 227, 257, 271, 347, 367, 557, 587, 607, 647, 727, 941 |
S |
| A046117 |
Primes p such that p-6 is also prime. |
11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137 |
S |
| A046086 |
|
3, 5, 8, 7, 20, 12, 9, 28, 11, 33, 16, 48, 36, 13, 39, 65, 20, 60, 15, 44 |
S |
| A046034 |
Numbers whose digits are primes. |
2, 3, 5, 7, 22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77 |
S |
| A045918 |
Describe n. Also called the "Say What You See" or "Look and Say" sequence LS(n). |
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1110, 21, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119 |
S |
| A045699 |
Numbers of the form p^2 + q^3, p,q prime. |
12, 17, 31, 33, 36, 52, 57, 76, 129, 134, 148, 150, 174, 177, 196, 246, 294, 297, 316, 347 |
S |
| A037074 |
Numbers that are the product of a pair of twin primes |
15, 35, 143, 323, 899, 1763, 3599, 5183, 10403, 11663, 19043, 22499, 32399, 36863, 39203, 51983, 57599, 72899, 79523, 97343 |
S |
| A036275 |
The periodic part of the decimal expansion of 1/n. Any initial 0's are to be placed at end of cycle. |
|
S |
| A035533 |
Number of numbers up to 10^n with exactly 4 divisors |
3, 32, 292, 2608, 23327 |
S |
| A034386 |
Primorial numbers (second definition): n# = product of primes <= n |
1, 1, 2, 6, 6, 30, 30, 210, 210, 210, 210, 2310, 2310, 30030, 30030, 30030, 30030, 510510, 510510, 9699690 |
S |
| A033948 |
numbers that have a primitive_root |
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 22, 23, 25, 26, 27 |
S |
| A033665 |
Number of 'Reverse and Add' steps needed to reach a palindrome starting at
n, or -1 if n never reaches a palindrome. |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2 |
S |
| A033492 |
Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A006877 |
1, 2, 8, 9, 17, 20, 21, 24, 112, 113, 116, 119, 122, 125, 128, 131, 144, 145, 171, 179 |
S |
| A033484 |
a(n)=3*2^n-2 |
1, 4, 10, 22, 46, 94, 190, 382, 766, 1534, 3070, 6142, 12286, 24574, 49150, 98302, 196606, 393214, 786430, 1572862 |
S |
| A031924 |
Lower prime of a difference of 6 between consecutive primes. |
23, 31, 47, 53, 61, 73, 83, 131, 151, 157, 167, 173, 233, 251, 257, 263, 271, 331, 353, 367 |
S |
| A030514 |
4th powers of primes. |
16, 81, 625, 2401, 14641, 28561, 83521, 130321, 279841, 707281, 923521, 1874161, 2825761, 3418801, 4879681, 7890481, 12117361, 13845841, 20151121, 25411681 |
S |
| A030513 |
Numbers with 4 divisors |
6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62 |
S |
| A030173 |
|
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 |
S |
| A030078 |
Cubes of primes |
8, 27, 125, 343, 1331, 2197, 4913, 6859, 12167, 24389, 29791, 50653, 68921, 79507, 103823, 148877, 205379, 226981, 300763, 357911 |
S |
| A027642 |
|
1, 2, 6, 1, 30, 1, 42, 1, 30, 1, 66, 1, 2730, 1, 6, 1, 510, 1, 798, 1 |
S |
| A027641 |
|
1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 5, 0, -691, 0, 7, 0, -3617, 0, 43867, 0 |
S |
| A024770 |
Right-truncatable primes: every prefix is prime. |
2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373 |
S |
| A024406 |
|
6, 30, 60, 84, 180, 210, 210, 330, 504, 546, 630, 840, 924, 990, 1224, 1320, 1386, 1560, 1710, 1716 |
S |
| A024023 |
a(n) = 3^n - 1. |
0, 2, 8, 26, 80, 242, 728, 2186, 6560, 19682, 59048, 177146, 531440, 1594322, 4782968, 14348906, 43046720, 129140162, 387420488, 1162261466 |
S |
| A023271 |
|
5, 11, 41, 61, 251, 601, 641, 1091, 1481, 1601, 1741, 1861, 2371, 2671, 3301, 3911, 4001, 5101, 5381, 5431 |
S |
| A023201 |
Sexy Primes : Numbers n such that n and n + 6 are both prime (sexy primes) |
5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131 |
S |
| A023200 |
Lesser of cousin primes. |
3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349 |
S |
| A023109 |
|
0, 10, 19, 59, 69, 166, 79, 188, 193, 1397, 829, 167, 2069, 1797, 849, 177, 1496, 739, 1798, 10777 |
S |
| A023108 |
Positive integers which apparently never result in a palindrome
|
196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978, 986, 1495, 1497, 1585, 1587, 1675, 1677, 1765 |
S |
| A023059 |
Numbers k such that k and 2k are anagrams of each other in base 4 (k is written here in base 4) |
102, 123, 1002, 1020, 1032, 1203, 1230, 1233, 1302, 1323, 10002, 10020, 10032, 10200, 10221, 10320, 10332, 11022, 11223, 12003 |
S |
| A023058 |
Numbers k such that k and 2k are anagrams of each other in base 3 (k is written here in base 3) |
1012, 10012, 10120, 10122, 10212, 100012, 100120, 100122, 100212, 101200, 101220, 101222, 102120, 102122, 102212, 1000012 |
S |
| A023052 |
Powerful numbers (3): numbers n that are the sum of some fixed power of their digits. |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 4150, 4151, 8208, 9474 |
S |
| A023001 |
a(n) = (8^n - 1)/7. |
0, 1, 9, 73, 585, 4681, 37449, 299593, 2396745, 19173961, 153391689, 1227133513, 9817068105, 78536544841, 628292358729, 5026338869833, 40210710958665, 321685687669321, 2573485501354569, 20587884010836553 |
S |
| A023000 |
a(n) = (7^n - 1)/6. |
0, 1, 8, 57, 400, 2801, 19608, 137257, 960800, 6725601, 47079208, 329554457, 2306881200, 16148168401, 113037178808, 791260251657, 5538821761600, 38771752331201, 271402266318408, 1899815864228857 |
S |
| A022005 |
Initial members of prime triples (p, p+4, p+6). |
7, 13, 37, 67, 97, 103, 193, 223, 277, 307, 457, 613, 823, 853, 877, 1087, 1297, 1423, 1447, 1483 |
S |
| A022004 |
Initial members of prime triples (p, p+2, p+6). |
5, 11, 17, 41, 101, 107, 191, 227, 311, 347, 461, 641, 821, 857, 881, 1091, 1277, 1301, 1427, 1481 |
S |
| A020882 |
|
5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 65, 73, 85, 85, 89, 97, 101, 109, 113, 125 |
S |
| A020639 |
Lpf(n): least prime dividing n (when n > 1); a(1) = 1. |
1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2 |
S |
| A020449 |
Primes that contain digits 0 and 1 only. |
11, 101, 10111, 101111, 1011001, 1100101, 10010101, 10011101, 10100011, 10101101, 10110011, 10111001, 11000111, 11100101, 11110111, 11111101, 100100111, 100111001, 101001001, 101001011 |
S |
| A018239 |
Primorial primes: form product of first k primes and add 1, then reject unless prime. |
2, 3, 7, 31, 211, 2311, 200560490131 |
S |
| A016957 |
a(n) = 6*n + 4. |
4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118 |
S |
| A016125 |
a(n) = (12^n - 1)/11. |
1, 13, 157, 1885, 22621, 271453, 3257437, 39089245, 469070941, 5628851293, 67546215517, 810554586205, 9726655034461, 116719860413533, 1400638324962397, 16807659899548765, 201691918794585181 |
S |
| A016123 |
a(n) = (11^n - 1)/10. |
1, 12, 133, 1464, 16105, 177156, 1948717, 21435888, 235794769, 2593742460, 28531167061, 313842837672, 3452271214393, 37974983358324, 417724816941565, 4594972986357216, 50544702849929377, 555991731349223148 |
S |
| A014080 |
Factorions: equal to the sum of the factorials of their digits in base 10. |
1, 2, 145, 40585 |
S |
| A010861 |
Describe the previous term! (method A - initial term is 22) |
22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22 |
S |
| A010060 |
Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 0 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 0's and 1's. |
0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1 |
S |
| A009996 |
Numbers with digits in nonincreasing order. |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40 |
S |
| A009994 |
Numbers with digits in nondecreasing order. |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22 |
S |
| A009096 |
|
12, 24, 30, 36, 40, 48, 56, 60, 60, 70, 72, 80, 84, 84, 90, 90, 96, 108, 112, 120 |
S |
| A008908 |
(1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached. |
1, 2, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, 18, 18, 5, 13, 21, 21, 8 |
S |
| A008683 |
Möbius (or Moebius) function mu(n). mu(1) = 1; mu(n) = (-1)^k if n is the product of k different primes; otherwise mu(n) = 0. |
1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0 |
S |
| A008589 |
Multiples of 7 |
0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133 |
S |
| A008587 |
Multiples of 5 |
0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 |
S |
| A008578 |
Prime numbers at the beginning of the 20th century (today 1 is no longer regarded as a prime). |
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 |
S |
| A008463 |
Take sum of squares of digits of previous term, starting with 9 |
9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16 |
S |
| A008462 |
Take sum of squares of digits of previous term, starting with 8 |
8, 64, 52, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37 |
S |
| A008460 |
Take sum of squares of digits of previous term, starting with 6 |
6, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42 |
S |
| A007953 |
Digital sum (i.e., sum of digits) of n; also called digsum(n). |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 |
S |
| A007770 |
Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1. |
1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100 |
S |
| A007529 |
Prime triples: n; n+2 or n+4; n+6 all prime. |
5, 7, 11, 13, 17, 37, 41, 67, 97, 101, 103, 107, 191, 193, 223, 227, 277, 307, 311, 347 |
S |
| A007510 |
Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime |
2, 23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 157, 163, 167, 173, 211, 223, 233 |
S |
| A007508 |
Number of twin prime pairs below 10^n. |
2, 8, 35, 205, 1224, 8169 |
S |
| A007505 |
Thabit primes of form 3*2^n -1. |
2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903 |
S |
| A007504 |
|
0, 2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281, 328, 381, 440, 501, 568 |
S |
| A007500 |
Primes whose reversal in base 10 is also prime |
2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 101, 107, 113, 131, 149, 151, 157 |
S |
| A007318 |
|
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5 |
S |
| A007088 |
The binary numbers: numbers written in base 2 |
0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011 |
S |
| A006960 |
|
196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, 18211171, 35322452, 60744805, 111589511, 227574622, 454050344, 897100798, 1794102596, 8746117567, 16403234045 |
S |
| A006883 |
Long period primes: the decimal expansion of 1/p has period p-1. |
2, 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229 |
S |
| A006881 |
Numbers that are the product of two distinct primes. |
6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69 |
S |
| A006877 |
In the `3x+1' problem, these values for the starting value set new records for number of steps to reach 1 |
1, 2, 3, 6, 7, 9, 18, 25, 27, 54, 73, 97, 129, 171, 231, 313, 327, 649, 703, 871 |
S |
| A006862 |
Euclid numbers: 1 + product of the first n primes. |
2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, 6469693231, 200560490131, 7420738134811, 304250263527211, 13082761331670031, 614889782588491411 |
S |
| A006751 |
Describe the previous term! (method A - initial term is 2). |
2, 12, 1112, 3112, 132112, 1113122112, 311311222112, 13211321322112 |
S |
| A006715 |
Describe the previous term! (method A - initial term is 3). |
3, 13, 1113, 3113, 132113, 1113122113, 311311222113, 13211321322113 |
S |
| A006567 |
Emirps (primes whose reversal is a different prime). |
13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389 |
S |
| A006530 |
Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1. |
1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5 |
S |
| A006521 |
Numbers n such that n divides 2^n + 1. |
1, 3, 9, 27, 81, 171, 243, 513, 729, 1539, 2187, 3249, 4617, 6561, 9747, 13203, 13851 |
S |
| A006512 |
Greater of twin primes. |
5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313 |
S |
| A006370 |
The Collatz or 3x+1 map: a(n) = n/2 if n is even, 3n + 1 if n is odd. |
0, 4, 1, 10, 2, 16, 3, 22, 4, 28, 5, 34, 6, 40, 7, 46, 8, 52, 9, 58 |
S |
| A005843 |
The even numbers: a(n) = 2n |
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38 |
S |
| A005728 |
Number of fractions in Farey series of order n. |
1, 2, 3, 5, 7, 11, 13, 19, 23, 29, 33, 43, 47, 59, 65, 73, 81, 97, 103, 121 |
S |
| A005541 |
Numbers n such that 8*3^n-1 is prime |
0, 1, 2, 4, 10, 17, 50, 170, 184, 194, 209, 641 |
S |
| A005408 |
The odd numbers: a(n) = 2n+1. |
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39 |
S |
| A005384 |
Sophie Germain primes p: 2p+1 is also prime. |
2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293 |
S |
| A005349 |
Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits. |
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42 |
S |
| A005234 |
Primorial primes: primes p such that 1 + product of primes up to p is prime |
2, 3, 5, 7, 11, 31, 379, 1019 |
S |
| A005188 |
Armstrong (or Plus Perfect, or narcissistic) numbers: n-digit numbers equal to sum of n-th powers of their digits |
0, 1, 2, 3, 4 |
S |
| A005151 |
Summarize the previous term! (in increasing order). |
1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314 |
S |
| A005150 |
Look and Say sequence: describe the previous term! (method A - initial term is 1). |
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221 |
S |
| A005132 |
|
0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62 |
S |
| A005117 |
|
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31 |
S |
| A005042 |
Primes formed by the initial digits of the decimal expansion of Pi. |
3, 31, 314159 |
S |
| A004169 |
Values of n for which a regular polygon with n sides cannot be constructed with ruler and compass |
7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 35, 36, 37 |
S |
| A004042 |
Periods of reciprocals of A006883, starting with first nonzero digit. |
|
S |
| A003945 |
Expansion of g.f. (1+x)/(1-2*x). |
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432 |
S |
| A003893 |
Fibonacci numbers modulo 10 |
0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1 |
S |
| A003592 |
Numbers of the form 2^i*5^j with i, j >= 0. |
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250 |
S |
| A003464 |
a(n) = (6^n - 1)/5. |
0, 1, 7, 43, 259, 1555, 9331, 55987, 335923, 2015539, 12093235, 72559411, 435356467, 2612138803, 15672832819, 94036996915, 564221981491, 3385331888947, 20311991333683, 121871948002099 |
S |
| A003463 |
a(n) = (5^n - 1)/4. |
0, 1, 6, 31, 156, 781, 3906, 19531, 97656, 488281, 2441406, 12207031, 61035156, 305175781, 1525878906, 7629394531, 38146972656, 190734863281, 953674316406, 4768371582031 |
S |
| A003462 |
a(n) = (3^n - 1)/2. |
0, 1, 4, 13, 40, 121, 364, 1093, 3280, 9841, 29524, 88573, 265720, 797161, 2391484, 7174453, 21523360, 64570081, 193710244, 581130733 |
S |
| A003401 |
Values of n for which a regular polygon with n sides can be constructed with ruler and compass |
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51 |
S |
| A003147 |
Primes with a fibonacci primitive root |
5, 11, 19, 31, 41, 59, 61, 71, 79, 109, 131, 149, 179 |
S |
| A003132 |
Sum of squares of digits of n. |
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82 |
S |
| A002779 |
Palindromic squares. |
0, 1, 4, 9, 121, 484, 676, 10201, 12321, 14641, 40804, 44944, 69696, 94249, 698896, 1002001, 1234321, 4008004, 5221225, 6948496 |
S |
| A002452 |
a(n) = (9^n - 1)/8. |
0, 1, 10, 91, 820, 7381, 66430, 597871, 5380840, 48427561, 435848050, 3922632451, 35303692060, 317733228541, 2859599056870, 25736391511831, 231627523606480, 2084647712458321, 18761829412124890, 168856464709124011 |
S |
| A002450 |
a(n) = (4^n - 1)/3. |
0, 1, 5, 21, 85, 341, 1365, 5461, 21845, 87381, 349525, 1398101, 5592405, 22369621, 89478485, 357913941, 1431655765, 5726623061, 22906492245, 91625968981 |
S |
| A002371 |
Period of decimal expansion of 1/(n-th prime) (0 by convention for the primes 2 and 5). |
0, 1, 0, 6, 2, 6, 16, 18, 22, 28, 15, 3, 5, 21, 46, 13, 58, 60, 33, 35 |
S |
| A002322 |
Reduced totient function psi(n): least k such that x^k == 1 (mod n) for all x prime to n also known as the Carmichael lambda function (exponent of unit group mod n) also called the universal exponent of n. |
1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 4, 4, 16, 6, 18, 4 |
S |
| A002275 |
Repunits: (10^n - 1)/9. Often denoted by R_n. |
0, 1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111 |
S |
| A002249 |
a(n) = a(n-1) - 2*a(n-2) with a(0) = 2, a(1) = 1. |
2, 1, -3, -5, 1, 11, 9, -13, -31, -5, 57, 67, -47, -181, -87, 275, 449, -101, -999, -797 |
S |
| A002235 |
Numbers n such that 3*2^n-1 is prime |
0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216 |
S |
| A002182 |
Highly composite numbers, definition (1): where d(n), the number of divisors of n (A000005), increases to a record. |
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560 |
S |
| A002110 |
Primorial numbers (first definition): product of first n primes |
1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410 |
S |
| A002093 |
Highly abundant numbers: numbers n such that sigma(n) > sigma(m) for all m < n. |
1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90 |
S |
| A002088 |
|
0, 1, 2, 4, 6, 10, 12, 18, 22, 28, 32, 42, 46, 58, 64, 72, 80, 96, 102, 120 |
S |
| A002064 |
Cullen numbers |
1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473 |
S |
| A001969 |
Evil numbers: numbers with an even number of 1's in their binary expansion. |
0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39 |
S |
| A001918 |
Least positive primitive root of n-th prime. ) |
1, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 6, 3, 5, 2, 2, 2, 2, 7 |
S |
| A001913 |
Primes with primitive root 10. |
7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233 |
S |
| A001771 |
Numbers n such that 7*2^n-1 is prime |
1, 5, 9, 17, 21, 29, 45, 177 |
S |
| A001694 |
powerful numbers |
1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169 |
S |
| A001477 |
The non-negative integers. |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 |
S |
| A001359 |
Lesser of twin primes. |
3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311 |
S |
| A001358 |
Semiprimes (or biprimes): products of two primes. |
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57 |
S |
| A001348 |
Mersenne numbers: 2^p - 1, where p is prime. |
3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 536870911, 2147483647, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487 |
S |
| A001318 |
Generalized pentagonal numbers: n*(3*n-1)/2, n=0, +- 1, +- 2, +- 3, .... |
0, 1, 2, 5, 7, 12, 15, 22, 26, 35, 40, 51, 57, 70, 77, 92, 100, 117, 126, 145 |
S |
| A001248 |
Square of primes |
4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041 |
S |
| A001223 |
Prime gaps: differences between consecutive primes. |
1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2 |
S |
| A001222 |
Number of prime divisors of n counted with multiplicity |
0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3 |
S |
| A001221 |
Number of distinct primes dividing n |
0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2 |
S |
| A001175 |
Pisano period |
1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60 |
S |
| A001155 |
Describe the previous term! (method A - initial term is 0). |
0, 10, 1110, 3110, 132110, 1113122110, 311311222110, 13211321322110 |
S |
| A001146 |
2^(2^n) |
2, 4, 16, 256, 65536, 4294967296 |
S |
| A001122 |
Primes with primitive root 2. |
3, 5, 11, 13, 19, 29, 37, 53, 59, 61, 67, 83, 101, 107, 131, 139, 149, 163, 173, 179 |
S |
| A001110 |
Square triangular numbers: numbers that are both triangular and square |
0, 1, 36, 1225, 41616, 1413721, 48024900, 1631432881, 55420693056, 1882672131025, 63955431761796, 2172602007770041, 73804512832419600 |
S |
| A001109 |
a(n)^2 is a triangular number |
0, 1, 6, 35, 204, 1189, 6930, 40391, 235416, 1372105, 7997214, 46611179, 271669860, 1583407981, 9228778026, 53789260175, 313506783024, 1827251437969, 10650001844790, 62072759630771 |
S |
| A001107 |
|
0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387 |
S |
| A001106 |
|
0, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089, 1216 |
S |
| A001101 |
Moran numbers: n such that (n / sum of digits of n) is prime.Called "Strong Harshad"in Euler Problem 387 |
18, 21, 27, 42, 45, 63, 84, 111, 114, 117, 133, 152, 153, 156, 171, 190, 195, 198, 201, 207 |
S |
| A001097 |
|
3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137 |
S |
| A001057 |
Canonical enumeration of integers: interleaved positive and negative integers with zero prepended. |
0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10 |
S |
| A001045 |
Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1. |
0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763 |
S |
| A000961 |
Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1). |
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37 |
S |
| A000931 |
Padovan sequence: a(n) = a(n-2) + a(n-3) with a(0)=1, a(1)=a(2)=0. |
1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37 |
S |
| A000796 |
Decimal expansion of Pi (or, digits of Pi).0 |
3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4 |
S |
| A000720 |
pi(n), the number of primes <= n. Sometimes called PrimePi(n) |
0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8 |
S |
| A000668 |
Mersenne primes (of form 2^p - 1 where p is a prime). |
3, 7, 31, 127, 8191, 131071, 524287, 2147483647 |
S |
| A000567 |
|
0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936, 1045 |
S |
| A000566 |
|
0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874 |
S |
| A000537 |
Sum of first n cubes; or n-th triangular number squared |
0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, 11025, 14400, 18496, 23409, 29241, 36100 |
S |
| A000396 |
Perfect numbers n: n is equal to the sum of the proper divisors of n. |
6, 28, 496, 8128, 33550336, 8589869056, 137438691328 |
S |
| A000384 |
:return: nth hexagonal number
:see: https://en.wikipedia.org/wiki/Hexagonal_number
|
0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703 |
S |
| A000332 |
Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24. |
0, 0, 0, 0, 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365, 1820, 2380, 3060, 3876 |
S |
| A000330 |
Square pyramidal numbers |
0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470 |
S |
| A000326 |
pentagonal numbers |
0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532 |
S |
| A000292 |
Tetrahedral (or triangular pyramidal) numbers |
0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330 |
S |
| A000290 |
squares |
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361 |
S |
| A000244 |
Powers of 3: a(n) = 3^n. |
1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467 |
S |
| A000225 |
a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348. |
0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287 |
S |
| A000221 |
Take sum of squares of digits of previous term, starting with 5 |
5, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58 |
S |
| A000218 |
Take sum of squares of digits of previous term, starting with 3 |
3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4 |
S |
| A000217 |
triangle numbers |
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190 |
S |
| A000216 |
Take sum of squares of digits of previous term, starting with 2 |
2, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37 |
S |
| A000215 |
Fermat numbers |
3, 5, 17, 257, 65537, 4294967297 |
S |
| A000203 |
sigma(n) = sum of divisors of n. |
1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42 |
S |
| A000196 |
Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times |
0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4 |
S |
| A000142 |
Factorial numbers: n! = 1*2*3*4*...*n order of symmetric group S_n, number of permutations of n letters. |
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000 |
S |
| A000129 |
Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2). |
0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109 |
S |
| A000120 |
1's-counting sequence: number of 1's in binary expansion of n |
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3 |
S |
| A000110 |
|
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057 |
S |
| A000108 |
Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).
|
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190 |
S |
| A000079 |
Powers of 2: a(n) = 2^n. |
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288 |
S |
| A000071 |
|
0, 0, 1, 2, 4, 7, 12, 20, 33, 54, 88, 143, 232, 376, 609, 986, 1596, 2583, 4180, 6764 |
S |
| A000045 |
Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. |
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181 |
S |
| A000043 |
Mersenne exponents: primes p such that 2^p - 1 is prime. |
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279 |
S |
| A000041 |
number of partitions of n (the partition numbers) |
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490 |
S |
| A000040 |
The prime numbers |
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 |
S |
| A000032 |
Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1. |
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349 |
S |
| A000027 |
The positive integers. |
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 |
S |
| A000010 |
Euler totient function
:see: http://stackoverflow.com/questions/1019040/how-many-numbers-below-n-are-coprimes-to-n
|
1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8 |
S |
| A000009 |
Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts (if n > 0). |
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54 |
S |
| A000007 |
The characteristic function of 0: a(n) = 0^n. |
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
S |
| A000006 |
Integer part of square root of n-th prime. |
1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8 |
S |
| A000005 |
d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n. |
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6 |
S |
| A000004 |
The zero sequence |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
S |