A360095 Decimal expansion of Sum_{p primes, p == 3 (mod 4)} log(p)/p^2.

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, 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, 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

Offset: 0

Author

Vaclav Kotesovec, Jan 25 2023

Keywords

• nonn
• cons

Examples

			0.212444768931665057705067792682825214870373695843766697810497537167709...
		

Links

• X. Gourdon and P. Sebah, Some Constants from Number theory.

Crossrefs

Cf. A085548, A085991, A086239, A136271, A358789, A360094.

Programs

Mathematica

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}]

Formula

Equals A136271 - A360094 - log(2)/4.