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A132184
Numbers k such that the numerator of the Bernoulli number B(2k) ends with the digits 691.
0
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
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
KEYWORD
base,nonn
AUTHOR
Alexander Adamchuk, Nov 04 2007
EXTENSIONS
a(5)-a(42) from Donovan Johnson, Sep 05 2008
STATUS
approved