A286854 Numbers k such that k == 1 or -1 (mod 6) but k does not divide the numerator of Bernoulli(2*k).

55, 253, 275, 385, 605, 715, 935, 1045, 1081, 1265, 1375, 1595, 1705, 1711, 1771, 1925, 2035, 2255, 2365, 2485, 2585, 2695, 2783, 2915, 3025, 3245, 3289, 3355, 3403, 3575, 3685, 3905, 4015, 4235, 4301, 4345, 4565, 4675, 4807, 4895, 5005, 5225, 5335, 5405, 5555

Offset: 1

Author

Bill Gosper, Aug 01 2017

Keywords

• nonn

Crossrefs

Cf. A000367, A286853 (1st differences).

Programs

Maple

isa := n -> abs(mods(n, 6)) = 1 and modp(numer(bernoulli(2*n)), n) <> 0:
select(isa, [$1..2255]); # Peter Luschny, Aug 02 2017

Mathematica

Select[Range@9999,0 != Mod[Numerator@BernoulliB[2 #], #] && MemberQ[{1, 5}, Mod[#, 6]] &]

PARI

isok(n) = (((n % 6) == 1) || ((n % 6) == 5)) && (numerator(bernfrac(2*n)) % n); \\ Michel Marcus, Aug 02 2017