A165361 Decimal expansion of log 2 times the negative of Granville-Soundararajan constant.

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

Offset

0,1

Comments

Given as formula and decimal expansion in p. 4 of Tao, citing Granville.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

A. Granville and K. Soundararajan, Negative values of truncations to L(1,chi), Analytic number theory: a tribute to Gauss and Dirichlet, Clay Math. Proc. Volume 7, 2007.

Terence Tao, A remark on partial sums involving the Mobius function, Bull. Aust. Math. Soc. 81 (2010), no. 2, 343-349.

Formula

Equals log(2)*A126689 = A002162*A126689.

Example

-0.455397....

Mathematica

RealDigits[ -Log[2]*(4*PolyLog[2, -Sqrt[E]] + Pi^2/3 + 1) , 10, 105] // First (* Jean-François Alcover, Feb 15 2013, after R. J. Mathar *)

Prog

(PARI) -log(2)*(Pi^2/3+4*polylog(2, -exp(1/2))+1) \\ Charles R Greathouse IV, Jul 18 2014
(Python)
from mpmath import mp, pi, sqrt, polylog, log
mp.dps=106
C = -log(2)*(4*polylog(2, -sqrt(e)) + pi**2/3 + 1)
print([int(n) for n in list(str(C)[2:-1])]) # Indranil Ghosh, Jul 03 2017

Crossrefs

Sequence in context: A029685 A153131 A016718 * A197136 A320475 A106626

Adjacent sequences: A165358 A165359 A165360 * A165362 A165363 A165364

Keyword

cons,nonn

Author

Jonathan Vos Post, Sep 16 2009

Extensions

More digits from R. J. Mathar, Sep 21 2009

Status

approved