A340440 Decimal expansion of Sum_{k>=2} log(k)/(k^2-1).

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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

R. J. Mathar, The series limit of sum_k 1/(k log k (log log k)^2), arXiv:0902.0789 [math.NA], 2009-2021, version 3, App. B.

Formula

Equals Sum_{i>=1} -zeta'(2i) = A073002 + A261506 - Sum_{i>=3} zeta'(2i).

Sum_{k>=2} log(k)/(k^2-s) = -Sum_{i>=1} s^(i-1)*zeta'(2i) for |s|<4. - R. J. Mathar, May 03 2021

Equals log(2)/2 + Sum_{k>=1} (zeta(2*k)-1)/(2*k-1). - Amiram Eldar, Jun 08 2021

Example

1.0231387264279392955...

Prog

(PARI) sumpos(k=2, log(k)/(k^2-1)) \\ Michel Marcus, Jan 09 2021

Crossrefs

Cf. A073002, A261506, A340485, A340484.

Sequence in context: A093768 A209419 A119011 * A300866 A130477 A226513

Adjacent sequences: A340437 A340438 A340439 * A340441 A340442 A340443

Keyword

nonn,cons

Author

R. J. Mathar, Jan 07 2021

Status

approved