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

1,1

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.

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Bernoulli Number.

Example

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.

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 *)

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).

Sequence in context: A164698 A020880 A046467 * A143322 A246544 A034897

Adjacent sequences: A132181 A132182 A132183 * A132185 A132186 A132187

Keyword

base,nonn

Author

Alexander Adamchuk, Nov 04 2007

Extensions

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

Status

approved