A092133 -id:A092133 - cp's OEIS frontend

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

10, 12, 14, 16, 18, 36, 42

Offset: 1

Eric W. Weisstein, Feb 23 2004

No others with k <= 22100. - Eric W. Weisstein, Mar 01 2004
a(8) > 50000. - Robert Price, Oct 20 2013
a(8) > 300000. - Serge Batalov, Jun 27 2025

Eric Weisstein's World of Mathematics, Bernoulli Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes

Cf. A092133.

Reap[For[n = 1, n <= 1000, n++, If[ PrimeQ[ Numerator[ BernoulliB[n]]], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2012 *)
Select[Range[50],PrimeQ[Numerator[BernoulliB[#]]]&] (* Harvey P. Dale, Sep 30 2019 *)

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

Original entry on oeis.org

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

Alexander Adamchuk, Nov 04 2007

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.

			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.

Eric Weisstein's World of Mathematics, Bernoulli Number.

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).

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 *)

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica