A382854 Decimal expansion of (1-log(2))/2.

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

Offset

0,2

References

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See exercise 109 at page 269.

Hari M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2012. See eq. (493), p. 313.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products (6th ed.), 2000, (eq. 0.238.2).

Formula

Equals Sum_{k>=1} (-1)^(k+1) / ((2*k-1) * 2*k * (2*k+1)).

Equals Sum_{k>=1} zeta(2*k)/((2*k+1)*4^k) (Srivastava and Choi, 2012). - Amiram Eldar, Aug 01 2025

Equals Integral_{x=0..1} Integral_{y=0..x} Integral_{z=0..y} 1/(1 + z^2) dz dy dx. - Kritsada Moomuang, Oct 03 2025

Example

0.15342640972002734529138393927091171596224993281987...

Maple

evalf[140]((1-log(2))/2);  # Alois P. Heinz, Apr 07 2025

Mathematica

First[RealDigits[(1 - Log[2])/2, 10, 100]] (* Paolo Xausa, Apr 07 2025 *)

Prog

(PARI) (1-log(2))/2 \\ Amiram Eldar, Aug 01 2025

Crossrefs

Cf. A187832, A372858, A382884.

Sequence in context: A090343 A135448 A243359 * A222229 A382499 A382680

Adjacent sequences: A382851 A382852 A382853 * A382855 A382856 A382857

Keyword

nonn,cons

Author

Sean A. Irvine, Apr 06 2025

Status

approved