cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A091216 Numbers k such that numerator of Bernoulli(2*k) is divisible by 37, the first irregular prime.

Original entry on oeis.org

16, 34, 37, 52, 70, 74, 88, 106, 111, 124, 142, 148, 160, 178, 185, 196, 214, 222, 232, 250, 259, 268, 286, 296, 304, 322, 333, 340, 358, 370, 376, 394, 407, 412, 430, 444, 448, 466, 481, 484, 502, 518, 520, 538, 555, 556, 574, 592, 610, 628
Offset: 1

Views

Author

N. J. A. Sloane, Feb 24 2004

Keywords

Links

Crossrefs

Cf. A000928, A092221, A092222, A092223, A092224, A092225, A092226, A092227, A092228, A092229, A092230, A092231.

Programs

  • Mathematica
    Select[ Range[ 681], Mod[ Numerator[ BernoulliB[2# ]], 37] == 0 &] (* Robert G. Wilson v, Feb 24 2004 *)
  • PARI
    for(j=1,260, if (! (numerator(bernfrac(2*j))%37), print1(j, ", ")))

Extensions

More terms from Robert G. Wilson v, Feb 24 2004

A092221 Numbers k such that numerator of Bernoulli(2*k) is divisible by 59, the second irregular prime.

Original entry on oeis.org

22, 51, 59, 80, 109, 118, 138, 167, 177, 196, 225, 236, 254, 283, 295, 312, 341, 354, 370, 399, 413, 428, 457, 472, 486, 515, 531, 544, 573, 590, 602, 631, 649, 660, 689, 708, 718, 747, 767, 776, 805, 826, 834, 863, 885, 892, 921, 944, 950, 979, 1003, 1008
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Comments

Satisfies a(n) = 2*a(n-3) - a(n-6) for n < 67. - Chai Wah Wu, May 28 2016

Links

Crossrefs

Cf. A000928, A091216, A092222, A092223, A092224, A092225, A092226, A092227, A092228, A092229, A092231.

Programs

  • Mathematica
    Select[ Range[ 1036], Mod[ Numerator[ BernoulliB[2# ]], 59] == 0 &]
  • PARI
    for(n=0, 10^3, if( numerator(bernfrac(2*n))%59==0, print1(n, ", ") ) ); \\ Joerg Arndt, May 29 2016
  • Python
    from sympy import bernoulli
A092221_list = [n for n in range(10**3) if not bernoulli(2*n).p % 59] # Chai Wah Wu, May 28 2016

A092229 Numbers k such that numerator of Bernoulli(2*k) is divisible by 257, the tenth irregular prime.

Original entry on oeis.org

82, 210, 257, 338, 466, 514, 594, 722, 771, 850, 978, 1028, 1106, 1234, 1285, 1362, 1490, 1542, 1618, 1746, 1799, 1874, 2002, 2056, 2130, 2258, 2313, 2386, 2514, 2570, 2642, 2770, 2827, 2898, 3026, 3084, 3154, 3282, 3341, 3410, 3538, 3598, 3666, 3794
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Links

Crossrefs

Cf. A000928, A091216, A092221, A092222, A092223, A092224, A092225, A092226, A092227, A092228.

Programs

  • Mathematica
    Select[ Range[ 3854], Mod[ Numerator[ BernoulliB[2# ]], 257] == 0 &]

A092222 Numbers k such that numerator of Bernoulli(2*k) is divisible by 67, the third irregular prime.

Original entry on oeis.org

29, 62, 67, 95, 128, 134, 161, 194, 201, 227, 260, 268, 293, 326, 335, 359, 392, 402, 425, 458, 469, 491, 524, 536, 557, 590, 603, 623, 656, 670, 689, 722, 737, 755, 788, 804, 821, 854, 871, 887, 920, 938, 953, 986, 1005, 1019, 1052, 1072, 1085, 1118, 1139
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Comments

n is a member iff either 2n == 58 (mod 66) or n = 67k. - T. D. Noe, Mar 22 2004

Links

Crossrefs

Cf. A000928, A091216, A092221, A092223, A092224, A092225, A092226, A092227, A092228, A092229.

Programs

  • Mathematica
    Select[ Range[ 1150], Mod[ Numerator[ BernoulliB[2# ]], 67] == 0 &]

A092223 Numbers k such that numerator of Bernoulli(2*k) is divisible by 101, the fourth irregular prime.

Original entry on oeis.org

34, 84, 101, 134, 184, 202, 234, 284, 303, 334, 384, 404, 434, 484, 505, 534, 584, 606, 634, 684, 707, 734, 784, 808, 834, 884, 909, 934, 984, 1010, 1034, 1084, 1111, 1134, 1184, 1212, 1234, 1284, 1313, 1334, 1384, 1414, 1434, 1484, 1515, 1534, 1584, 1616
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Links

Crossrefs

Cf. A000928, A091216, A092221, A092222, A092224, A092225, A092226, A092227, A092228, A092229.

Programs

  • Mathematica
    Select[ Range[ 1633], Mod[ Numerator[ BernoulliB[2# ]], 101] == 0 &]

A092224 Numbers k such that the numerator of Bernoulli(2*k) is divisible by 103, the fifth irregular prime.

Original entry on oeis.org

12, 63, 103, 114, 165, 206, 216, 267, 309, 318, 369, 412, 420, 471, 515, 522, 573, 618, 624, 675, 721, 726, 777, 824, 828, 879, 927, 930, 981, 1030, 1032, 1083, 1133, 1134, 1185, 1236, 1287, 1338, 1339, 1389, 1440, 1442, 1491, 1542, 1545, 1593, 1644, 1648
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Comments

103 = A094095(1) is the first irregular prime in A094095. This sequence is the union of 2 arithmetic progressions: (24 + 102*n)/2 and 103*n. Note that the numerator of BernoulliB(2*114) is divisible by the first nontrivial irregular squared prime 103^2, when A090943(1)/2 = a(n) = 114 = (24 + 102*2)/2. Also, the numerator of BernoulliB(2*1236) is divisible by 103^2 because a(n) = 1236 = (24 + 102*24)/2 = 103*24/2. - Alexander Adamchuk, Jul 31 2006

Links

Crossrefs

Cf. A000928, A091216, A092221, A092222, A092223, A092225, A092226, A092227, A092228, A092229.
Cf. A094095, A090943, A027641.

Programs

  • Mathematica
    Select[ Range[ 1694], Mod[ Numerator[ BernoulliB[2# ]], 103] == 0 &]
Select[Union[Table[2n*103,{n,1,100}],Table[24+102*n,{n,0,100}]], #<=10000&]/2 (* Alexander Adamchuk, Jul 31 2006 *)

A092225 Numbers k such that numerator of Bernoulli(2*k) is divisible by 131, the sixth irregular prime.

Original entry on oeis.org

11, 76, 131, 141, 206, 262, 271, 336, 393, 401, 466, 524, 531, 596, 655, 661, 726, 786, 791, 856, 917, 921, 986, 1048, 1051, 1116, 1179, 1181, 1246, 1310, 1311, 1376, 1441, 1506, 1571, 1572, 1636, 1701, 1703, 1766, 1831, 1834, 1896, 1961, 1965, 2026, 2091
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Links

Crossrefs

Cf. A000928, A091216, A092221, A092222, A092223, A092224, A092226, A092227, A092228, A092229.

Programs

  • Mathematica
    Select[ Range[ 2095], Mod[ Numerator[ BernoulliB[2# ]], 131] == 0 &]

A092227 Numbers k such that numerator of Bernoulli(2*k) is divisible by 157, the eighth irregular prime and first irregular prime of index 2.

Original entry on oeis.org

31, 55, 109, 133, 157, 187, 211, 265, 289, 314, 343, 367, 421, 445, 471, 499, 523, 577, 601, 628, 655, 679, 733, 757, 785, 811, 835, 889, 913, 942, 967, 991, 1045, 1069, 1099, 1123, 1147, 1201, 1225, 1256, 1279, 1303, 1357, 1381, 1413, 1435, 1459, 1513, 1537
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Links

Crossrefs

Cf. A000928, A073277, A091216, A092221, A092222, A092223, A092224, A092225, A092226, A092228, A092229.

Programs

  • Mathematica
    Select[ Range[ 1569], Mod[ Numerator[ BernoulliB[2# ]], 157] == 0 &]

A092228 Numbers k such that numerator of Bernoulli(2*k) is divisible by 233, the ninth irregular prime.

Original entry on oeis.org

42, 158, 233, 274, 390, 466, 506, 622, 699, 738, 854, 932, 970, 1086, 1165, 1202, 1318, 1398, 1434, 1550, 1631, 1666, 1782, 1864, 1898, 2014, 2097, 2130, 2246, 2330, 2362, 2478, 2563, 2594, 2710, 2796, 2826, 2942, 3029, 3058, 3174, 3262, 3290, 3406, 3495
Offset: 1

Views

Author

Robert G. Wilson v, Feb 25 2004

Keywords

Links

Crossrefs

Cf. A000928, A091216, A092221, A092222, A092223, A092224, A092225, A092226, A092227, A092229.

Programs

  • Mathematica
    Select[ Range[ 3521], Mod[ Numerator[ BernoulliB[2# ]], 233] == 0 &]
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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