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A344716 Decimal expansion of (gamma + log(4/Pi))/2, where gamma is Euler's constant. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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]

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: A200591 A133844 A198238 * A187377 A187155 A187296

Adjacent sequences:  A344713 A344714 A344715 * A344717 A344718 A344719

KEYWORD

nonn,cons

AUTHOR

Kevin Ryde, May 27 2021

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)