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

Author

Jonathan Vos Post, Sep 16 2009

Keywords

• cons
• nonn

Comments

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

Examples

			-0.455397....
		

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.

Programs

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 *)

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

Formula

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

Extensions

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