A387303 Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(4*n)/(4*n), where P(x) is the prime zeta function.
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, 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, 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
Offset: 0
Examples
0.0187602016899806686319119770449145568...
Programs
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Mathematica
RealDigits[Log[105^(1/4)/Pi], 10, 105, -1][[1]]
Formula
Equals log(105^(1/4)/Pi).
For m > 1, Sum_{k>=1} (-1)^(k+1) * primezeta(m*k)/k = log(zeta(m)/zeta(2*m)). - Vaclav Kotesovec, Aug 25 2025