%I #30 Apr 28 2014 15:57:53
%S 5,15,25,35,45,55,65,75,85,95,105,115,125,135,145,155,165,185,195,205,
%T 215,225,235,245,255,265,275,285,295,305,315,335,345,355,365,375,395,
%U 405,415,445,455,465,475,485,495,505,515,525,535,545,555,565,575,585
%N 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.
%C 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).
%H Vaclav Kotesovec, <a href="/A068528/b068528.txt">Table of n, a(n) for n = 1..4473</a>
%H Vaclav Kotesovec, <a href="/A068528/a068528.jpg">Graph of a(n)/n</a>. Limit of a(n)/n (if it exists) is not 10, but ~11.18...
%e 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.
%e 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.
%e 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.
%t Select[10Range[0, 60] + 5, GCD[Numerator[BernoulliB[2#]], Denominator[BernoulliB[2# - 2]]] == 5 &] (* _Harvey P. Dale_, Apr 08 2013 *)
%Y Cf. A007703.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_ and _Labos Elemer_, Mar 21 2002