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%I #11 Mar 02 2023 21:25:23
%S 2,1,2,4,4,4,7,6,8,9,3,1,6,6,5,0,5,7,7,0,5,0,6,7,7,9,2,6,8,2,8,2,5,2,
%T 1,4,8,7,0,3,7,3,6,9,5,8,4,3,7,6,6,6,9,7,8,1,0,4,9,7,5,3,7,1,6,7,7,0,
%U 9,5,9,7,6,0,2,0,8,1,1,5,3,5,8,9,6,1,3,7,0,5,9,6,1,4,0,7,4,3,8,3,3,7,4,4,7,3
%N Decimal expansion of Sum_{p primes, p == 3 (mod 4)} log(p)/p^2.
%H X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.html">Some Constants from Number theory</a>.
%F Equals A136271 - A360094 - log(2)/4.
%e 0.212444768931665057705067792682825214870373695843766697810497537167709...
%t beta[s_]:= (1 - 1/2^s) * Zeta[s] / DirichletBeta[s]; Do[Print[N[-1/2*Sum[MoebiusMu[2*n + 1]/(2*n + 1) * D[Log[beta[(2*n + 1)*s]], s] /. s->2, {n, 0, m}], 120]], {m, 10, 100, 10}]
%Y Cf. A085548, A085991, A086239, A136271, A358789, A360094.
%K nonn,cons
%O 0,1
%A _Vaclav Kotesovec_, Jan 25 2023
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