OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.
FORMULA
Equals EulerGamma/12 + 1/24*(Pi*(2+sqrt(3)) - 2*(sqrt(3)-1)*log(2) + log(3) + 4*sqrt(3) * log(sqrt(3)+1)).
Equals Sum_{n>=0} (1/(12n+1) - 1/12*log((12n+13)/(12n+1))).
Equals -(psi(1/12) + log(12))/12. - Amiram Eldar, Jan 07 2024
EXAMPLE
0.83024988988662433938903419703214965055579639279727496201543...
MATHEMATICA
RealDigits[-Log[12]/12 - PolyGamma[1/12]/12, 10, 103] // First
PROG
(PARI) default(realprecision, 100); Euler/12 + 1/24*(Pi*(2+sqrt(3)) - 2*(sqrt(3)-1)*log(2) + log(3) + 4*sqrt(3)*log(sqrt(3)+1)) \\ G. C. Greubel, Aug 28 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/12 + (1/24)*(Pi(R)*(2+Sqrt(3)) - 2*(Sqrt(3)-1)*Log(2) + Log(3) + 4*Sqrt(3)*Log(Sqrt(3)+1)); // G. C. Greubel, Aug 28 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 10 2015
STATUS
approved