A068206 - OEIS

A068206

Let N(2n) denote the numerator of B(2n), the 2n-th Bernoulli number and D(2n) the denominator; sequence gives values of n such that gcd(N(2n),D(2n-2))=7.

%I #25 Apr 29 2014 09:22:35

%S 7,28,49,70,112,133,154,196,217,238,259,280,301,322,343,364,406,427,

%T 448,469,490,511,553,574,658,679,700,721,742,763,784,826,847,868,889,

%U 910,931,952,973,994,1036,1057,1078,1099,1120,1141,1162,1204,1246,1267

%N Let N(2n) denote the numerator of B(2n), the 2n-th Bernoulli number and D(2n) the denominator; sequence gives values of n such that gcd(N(2n),D(2n-2))=7.

%C a(n)==0 (mod 7). - _Labos Elemer_

%C Conjecture: All terms are of the form 7 + 21*j. - _Vaclav Kotesovec_, Apr 29 2014

%H Vaclav Kotesovec, <a href="/A068206/b068206.txt">Table of n, a(n) for n = 1..4048</a>

%H Vaclav Kotesovec, <a href="/A068206/a068206_1.jpg">Graph of a(n)/n</a>. Limit of a(n)/n (if it exists) is not 21, but ~ 25.9...

%t Select[21*Range[0,100]+7,GCD[Numerator[BernoulliB[2#]],Denominator[BernoulliB[2#-2]]]==7&] (* _Vaclav Kotesovec_, Apr 29 2014 *)

%o (PARI) isok(n) = gcd(numerator(bernfrac(2*n)), denominator(bernfrac(2*n-2))) == 7; \\ _Michel Marcus_, Mar 06 2014

%Y Cf. A068528.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Mar 23 2002