cp's OEIS Frontend

A387303 Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(4*n)/(4*n), where P(x) is the prime zeta function.

%I A387303 #10 Aug 28 2025 21:22:10
%S A387303 0,1,8,7,6,0,2,0,1,6,8,9,9,8,0,6,6,8,6,3,1,9,1,1,9,7,7,0,4,4,9,1,4,5,
%T A387303 5,6,8,0,5,2,4,9,3,4,7,5,0,2,9,7,0,5,1,9,0,1,3,0,6,0,0,2,2,2,9,0,1,7,
%U A387303 5,5,1,6,0,3,4,7,5,7,9,2,0,0,3,9,2,2,8,7,6,2,5,9,8,2,0,6,0,9,8,9,4,3,2,3,9
%N A387303 Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(4*n)/(4*n), where P(x) is the prime zeta function.
%F A387303 Equals log(105^(1/4)/Pi).
%F A387303 For m > 1, Sum_{k>=1} (-1)^(k+1) * primezeta(m*k)/k = log(zeta(m)/zeta(2*m)). - _Vaclav Kotesovec_, Aug 25 2025
%e A387303 0.0187602016899806686319119770449145568...
%t A387303 RealDigits[Log[105^(1/4)/Pi], 10, 105, -1][[1]]
%Y A387303 Cf. A387289, A387293, A387300.
%K A387303 nonn,cons,new
%O A387303 0,3
%A A387303 _Artur Jasinski_, Aug 25 2025