A344716 Decimal expansion of (gamma + log(4/Pi))/2, where gamma is Euler's constant.

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

Offset

0,1

Links

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

Jean-Paul Allouche, Jeffrey Shallit, and Jonathan Sondow, Summation of Series Defined by Counting Blocks of Digits, Journal of Number Theory, volume 123, number 1, March 2007, pages 133-143. Also arXiv:math/0512399 [math.NT], 2005-2006.

Formula

Equals (A001620 + A094640)/2, the mean of Euler's constant and alternating Euler's constant.

Equals Sum_{n>=1} A000120(n) / (2*n*(2*n+1)), where A000120 is the number of 1-bits of n in binary. [Allouche, Shallit, Sondow]

Equals Sum_{k>=1} (1/(2*k-1) - log(1+1/(2*k-1))). - Amiram Eldar, Jun 19 2023

Example

0.40939007008601165264877449082284842...

Mathematica

RealDigits[(EulerGamma + Log[4/Pi])/2, 10, 100][[1]] (* Amiram Eldar, May 27 2021 *)

Crossrefs

Cf. A001620, A094640, A000120.

Sequence in context: A133844 A198238 A380776 * A187377 A187155 A187296

Adjacent sequences: A344713 A344714 A344715 * A344717 A344718 A344719

Keyword

nonn,cons

Author

Kevin Ryde, May 27 2021

Status

approved