A068528 Let N(2k) denote the numerator of B(2k), the 2k-th Bernoulli number, and D(2k) the denominator; sequence gives values of k such that gcd(N(2k),D(2k-2))=5.

5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 185, 195, 205, 215, 225, 235, 245, 255, 265, 275, 285, 295, 305, 315, 335, 345, 355, 365, 375, 395, 405, 415, 445, 455, 465, 475, 485, 495, 505, 515, 525, 535, 545, 555, 565, 575, 585

Offset

1,1

Comments

All terms are of the form 5 + 10*j. In most cases, a(n+1) - a(n) = 10, but there are some jumps; e.g., a(18) - a(17) = 185 - 165 = 20 (see Examples).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..4473

Vaclav Kotesovec, Graph of a(n)/n. Limit of a(n)/n (if it exists) is not 10, but ~11.18...

Example

k=7: B(14)=7/6, B(12)=-691/2730, so gcd(N(14),D(12)) = gcd(7,2730) = 7; thus, k=7 is not in the sequence.
k=15: B(30)=8615841276005/14322, B(28)=-23749461029/870, so gcd(N(30),D(28)) = gcd(8615841276005,870) = 5; thus, k=15 is in the sequence.
k=175: N(350) is a large multiple of 35, D(348)=56213430, and gcd(N(350),D(348)) = 35; thus, k=175 is not in the sequence.

Mathematica

Select[10Range[0, 60] + 5, GCD[Numerator[BernoulliB[2#]], Denominator[BernoulliB[2# - 2]]] == 5 &] (* Harvey P. Dale, Apr 08 2013 *)

Crossrefs

Cf. A007703.

Sequence in context: A172404 A031322 A017329 * A061443 A168010 A353613

Adjacent sequences: A068525 A068526 A068527 * A068529 A068530 A068531

Keyword

easy,nonn

Author

Benoit Cloitre and Labos Elemer, Mar 21 2002

Status

approved