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

0,3

Links

Table of n, a(n) for n=0..104.

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

Example

0.0187602016899806686319119770449145568...

Mathematica

RealDigits[Log[105^(1/4)/Pi], 10, 105, -1][[1]]

Crossrefs

Cf. A387289, A387293, A387300.

Sequence in context: A388833 A201666 A349250 * A215737 A394599 A154718

Adjacent sequences: A387300 A387301 A387302 * A387304 A387305 A387306

Keyword

nonn,cons

Author

Artur Jasinski, Aug 25 2025

Status

approved