cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A366349 Decimal expansion of the Sum_{k>=1} (-1)^(k+1)*log(2*k)/(2*k).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Oct 07 2023

Keywords

Comments

For Sum_{k>=1} (-1)^(k+1)*log(2*k+1)/(2*k+1) see A078127.

Examples

			0.16029205508788522645507732800087420061716546391...
		

Crossrefs

Programs

  • Maple
    (3*(log(2))^2-2*gamma*log(2))/4; evalf(%) ; # R. J. Mathar, Jun 10 2024
  • Mathematica
    RealDigits[(3 Log[2]^2 - 2 EulerGamma Log[2])/4, 10, 106][[1]]
  • PARI
    sumalt(k=1, (-1)^(k+1)*log(2*k)/(2*k)) \\ Vaclav Kotesovec, Oct 08 2023

Formula

Equals (3*(log(2))^2-2*gamma*log(2))/4, where gamma is Euler gamma constant A001620.

A373562 Decimal expansion of Sum_{k>=0} (-1)^(k+1)*( log(2k+1)/(2k+1) + log(2k+2)/(2k+2) ).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Jun 10 2024

Keywords

Examples

			0.03260926170902720290811243602...
		

Crossrefs

Programs

  • Mathematica
    RealDigits[Pi*(EulerGamma + 2*Log[2] + 3*Log[Pi] - 4*Log[Gamma[1/4]])/4 - (3 Log[2]^2 - 2 EulerGamma Log[2])/4, 10, 120, -1][[1]] (* Amiram Eldar, Jun 10 2024 *)

Formula

Equals A078127 - A366349.
Showing 1-2 of 2 results.