A363687 Decimal expansion of Sum_{k>=1} cos(Pi* log k)/k^2.

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

Offset

0,1

Comments

Sum_{k>=1} sin(Pi*log k)/k^2 = 0.0942944615085... is the associated imaginary part.

Links

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

Math StackExchange, Closed form for sum n>=1 cos(pi*log(n)/n^2, (2013).

Formula

Equals Re(zeta(2 + Pi*i)), where i=sqrt(-1).

Example

0.795640206735677517430628328498...

Maple

Re(Zeta(2+I*Pi)) ;
evalf(%) ;

Mathematica

RealDigits[Re[Zeta[2 + Pi*I]], 10, 105][[1]] (* Amiram Eldar, Jun 16 2023 *)

Prog

(PARI) real(zeta(2+I*Pi)) \\ Michel Marcus, Jun 15 2023

Crossrefs

Sequence in context: A070693 A369095 A198417 * A215736 A132715 A154910

Adjacent sequences: A363684 A363685 A363686 * A363688 A363689 A363690

Keyword

cons,nonn

Author

R. J. Mathar, Jun 15 2023

Status

approved