A132184 Numbers k such that the numerator of the Bernoulli number B(2k) ends with the digits 691.

6, 21, 27, 321, 1266, 1527, 1821, 2526, 2576, 2721, 2950, 3126, 3246, 3426, 4206, 4236, 4821, 4926, 5286, 5721, 5946, 5950, 6100, 6351, 7018, 7138, 7172, 7386, 7806, 7931, 8037, 8790, 8796, 8826, 9021, 9048, 9426, 9478, 9726, 9921, 10221, 10326

Offset: 1

Author

Alexander Adamchuk, Nov 04 2007

Keywords

• base
• nonn

Comments

The numerator of BernoulliB(12) is 691. The sequence gives semi-indices of the 691-automorphic numerators in the BernoulliB(n) sequence. All 4 initial terms are multiples of 3. Note that Bernoulli numerators corresponding to the first two terms are the automorphic primes: 691 and 1520097643918070802691.

Examples

			6 is a term because BernoulliB(2*6) = -691/2730.
21 is a term because BernoulliB(2*21) = 1520097643918070802691/1806.
27 is a term because BernoulliB(2*27) = 29149963634884862421418123812691/798.
		

Links

• Eric Weisstein's World of Mathematics, Bernoulli Number.

Crossrefs

Cf. A000367 (numerators of Bernoulli numbers B_2n).

Cf. A092132 (indices k of Bernoulli numbers B(k) whose numerators are primes).

Cf. A092133 (prime numerators of Bernoulli numbers).

Programs

Mathematica

Do[ g=Numerator[ BernoulliB[ 2n ] ]; f=Mod[ Abs[ g ], 1000 ]; If[ f==691, Print[ n ] ], {n,1,1000}]
Select[Range[10400],Mod[Abs[Numerator[BernoulliB[2#]]],1000]==691&] (* Harvey P. Dale, May 05 2019 *)

Extensions

a(5)-a(42) from Donovan Johnson, Sep 05 2008