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

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, 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, 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

Offset: 0

Author

Vaclav Kotesovec, Jan 25 2023

Keywords

• nonn
• cons

Examples

			0.107359545297113077138450382009121901166339396912637779372659580780278...
		

Links

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

Crossrefs

Cf. A085548, A086032, A086239, A136271, A358789, A360095.

Programs

Mathematica

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}]

Formula

Equals A136271 - A360095 - log(2)/4.