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A360094 Decimal expansion of Sum_{p primes, p == 1 mod 4} log(p)/p^2.

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%I A360094 #9 Jan 25 2023 10:01:19
%S A360094 1,0,7,3,5,9,5,4,5,2,9,7,1,1,3,0,7,7,1,3,8,4,5,0,3,8,2,0,0,9,1,2,1,9,
%T A360094 0,1,1,6,6,3,3,9,3,9,6,9,1,2,6,3,7,7,7,9,3,7,2,6,5,9,5,8,0,7,8,0,2,7,
%U A360094 8,7,7,0,5,8,5,0,7,3,6,8,7,8,6,3,9,9,6,4,6,6,5,0,7,6,5,7,2,0,1,0,1,9,5,1,4,1
%N A360094 Decimal expansion of Sum_{p primes, p == 1 mod 4} log(p)/p^2.
%H A360094 X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.html">Some Constants from Number theory</a>.
%F A360094 Equals A136271 - A360095 - log(2)/4.
%e A360094 0.107359545297113077138450382009121901166339396912637779372659580780278...
%t A360094 alfa[s_]:= 1/(1 + 1/2^s) * DirichletBeta[s] * Zeta[s] / Zeta[2*s]; Do[Print[N[-1/2*Sum[MoebiusMu[2*n + 1]/(2*n + 1) * D[Log[alfa[(2*n + 1)*s]], s] /. s->2, {n, 0, m}], 120]], {m, 10, 100, 10}]
%Y A360094 Cf. A085548, A086032, A086239, A136271, A358789, A360095.
%K A360094 nonn,cons
%O A360094 0,3
%A A360094 _Vaclav Kotesovec_, Jan 25 2023