A079295 (D(p)-6)/(12p) where D(p) denotes the denominator of the 2p-th Bernoulli number and p runs through the primes.

1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset

1,1

Comments

If p is a Sophie Germain prime (A005384) then denominator(B(2p))= 6*(2p+1).

Links

Table of n, a(n) for n=1..95.

Formula

a(A053176(n))=0; a(A005384(n))=1.

a(n) = pi(2*prime(n) + 1) - pi(2*prime(n)), where pi(n) = A000720(n) and prime(n) = A000040(n). - Ridouane Oudra, Sep 02 2019

Mathematica

dbn[n_]:=Module[{d=Denominator[BernoulliB[2n]]}, (d-6)/(12n)]; dbn/@ Prime[ Range[100]] (* Harvey P. Dale, May 19 2012 *)

Prog

(PARI) a(n) = my(p=prime(n)); (denominator(bernfrac(2*p)) - 6)/(12*p); \\ Michel Marcus, Sep 02 2019

Crossrefs

Cf. A002445, A053176, A005384, A000040, A000720.

Sequence in context: A341540 A214507 A093709 * A088025 A192687 A189141

Adjacent sequences: A079292 A079293 A079294 * A079296 A079297 A079298

Keyword

nonn

Author

Benoit Cloitre, Feb 09 2003

Status

approved