This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358789 #79 Jan 26 2023 05:27:17
%S A358789 5,4,5,6,8,1,2,7,2,7,9,5,1,2,7,9,0,1,4,8,9,5,3,2,3,8,3,3,8,0,0,4,0,3,
%T A358789 8,3,4,7,5,2,5,2,8,0,5,4,1,4,2,7,4,4,6,5,4,0,7,5,9,8,6,6,3,9,2,8,8,7,
%U A358789 3,6,5,3,1,4,8,7,2,7,2,6,4,0,9,6,2,8,7,8,6,2,1,5,1,4,1,6,1,2,3,2,3,8,8,5,7,9,2,6,6,6,6,2,1,9,0
%N A358789 Decimal expansion of Sum_{p prime, p>=3} (-1)^((p-1)/2)*log(p)/p, negated.
%C A358789 Sum_{p prime} log(p)/p is divergent.
%F A358789 Limit_{N->oo} ((Sum_{p<=N prime == 3 (mod 4)} log(p)/p) - (Sum_{p<=N prime == 1 (mod 4)} log(p)/p)).
%e A358789 -0.54568127279512790148953238338...
%t A358789 alfa[s_]:= 1/(1 + 1/2^s) * DirichletBeta[s] * Zeta[s] / Zeta[2*s]; beta[s_]:= (1 - 1/2^s) * Zeta[s] / DirichletBeta[s]; Do[Print[N[-1/2*Sum[MoebiusMu[2*n + 1]/(2*n + 1) * Limit[D[Log[alfa[(2*n + 1)*s]/beta[(2*n + 1)*s]], s], s -> 1], {n, 0, m}], 120]], {m, 20, 200, 20}] (* _Vaclav Kotesovec_, Jan 25 2023 *)
%Y A358789 Cf. A086239, A091812, A136271, A354295.
%K A358789 nonn,cons
%O A358789 0,1
%A A358789 _Artur Jasinski_, Jan 03 2023