A387300 Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(2*n)/(2*n), where P(x) is the prime zeta function.

2, 0, 9, 2, 9, 5, 2, 1, 4, 7, 0, 1, 7, 0, 4, 8, 5, 8, 8, 5, 4, 5, 7, 4, 9, 3, 3, 7, 2, 1, 2, 9, 7, 9, 6, 0, 4, 3, 9, 2, 5, 1, 1, 4, 3, 1, 3, 0, 3, 2, 2, 0, 1, 5, 3, 1, 0, 0, 4, 8, 0, 4, 1, 0, 8, 3, 6, 9, 8, 8, 7, 0, 5, 7, 8, 3, 0, 7, 2, 8, 5, 9, 6, 8, 2, 5, 1, 5, 4, 6, 1, 7, 7, 9, 6, 6, 1, 4, 2, 0, 9, 1, 9, 5, 8

Offset

0,1

Links

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

Formula

Equals log(sqrt(15)/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

0.20929521470170485885457493372...

Mathematica

RealDigits[Log[Sqrt[15]/Pi], 10, 105][[1]]

Crossrefs

Cf. A387289, A387293, A387303.

Sequence in context: A248897 A021482 A199287 * A198735 A071120 A249417

Adjacent sequences: A387297 A387298 A387299 * A387301 A387302 A387303

Keyword

nonn

Author

Artur Jasinski, Aug 25 2025

Status

approved