A340808 - OEIS

%I #24 Jan 27 2021 13:09:44

%S 1,0,0,0,0,6,9,8,7,2,8,3,2,1,8,4,2,6,1,4,1,4,1,9,6,3,5,2,6,4,6,0,0,6,

%T 2,5,1,5,3,2,3,6,8,1,4,6,7,9,6,1,5,3,4,0,6,2,7,2,4,3,4,4,3,2,6,2,7,1,

%U 4,9,4,0,1,4,0,6,7,9,6,8,5,8,7,0,9,5,2,1,5,1,1,7,9,4,1,7,3,0,2,0,1,8,9,4,0

%N Decimal expansion of Product_{primes p == 1 (mod 5)} 1/(1-p^(-4)).

%C Equals also the same product over the primes p == 1 (mod 10).

%H Vaclav Kotesovec, <a href="/A340808/b340808.txt">Table of n, a(n) for n = 1..500</a>

%H R. J. Mathar, <a href="https://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and prime zeta modulo functions...</a> arXiv:1008.2547, Zeta_{m=5,n=1}(s=4).

%F A340629 = A340004 ^2 / this.

%F Equals Sum_{k>=1} 1/A004615(k)^4. - _Amiram Eldar_, Jan 24 2021

%e 1.0000698728321842614141963526460062515  = (14641/14640) * (923521/923520) * (2825761/2825760) *...

%Y Cf. A004615, A030430, A340004 (s=2), A340629, A340809, A340926, A340927.

%K nonn,cons

%O 1,6

%A _R. J. Mathar_, Jan 22 2021

%E More digits from _Vaclav Kotesovec_, Jan 22 2021