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

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

Author

Robert G. Wilson v, Feb 25 2004

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..6450 (terms 1..1000 from Joerg Arndt)
• Eric Weisstein's World of Mathematics, Bernoulli Number.

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