A375509 Decimal expansion of the negated derivative P'(3/2) of the prime zeta function at 3/2.

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

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Formula

P'(3/2) = -Sum_{p = 2,3,5,7,11,..} log(p)/p^(3/2) = -1.29571075479160755372...

Example

1.29571075479160755372288832464555766349416294698452...

Mathematica

$MaxExtraPrecision = 100; RealDigits[N[PrimeZetaP'[3/2], 120]][[1]] (* Amiram Eldar, Aug 19 2024 *)

Crossrefs

Cf. A338574 (P(3/2)), A136271 (P'(2)).

Sequence in context: A051491 A339204 A253169 * A373495 A339925 A171052

Adjacent sequences: A375506 A375507 A375508 * A375510 A375511 A375512

Keyword

nonn,cons

Author

R. J. Mathar, Aug 18 2024

Status

approved