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A165361
Decimal expansion of log 2 times the negative of Granville-Soundararajan constant.
1
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
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
KEYWORD
cons,nonn
AUTHOR
Jonathan Vos Post, Sep 16 2009
EXTENSIONS
More digits from R. J. Mathar, Sep 21 2009
STATUS
approved