OFFSET
0,1
COMMENTS
Equals the value of the Dirichlet L-series of a non-principal character modulo 12 (A110161) at s=1.
REFERENCES
L. B. W. Jolley, Summation of series, Dover (1961), eq. (83), page 16.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017.
E. D. Krupnikov, K. S. Kolbig, Some special cases of the generalized hypergeometric function (q+1)Fq, J. Comp. Appl. Math. 78 (1997) 79-95
R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, Table in section 2.2, L(m=12,r=4,s=1).
FORMULA
Equals Sum_{n>=1} A110161(n)/n.
Equals Sum_{k>=1} (-1)^(k+1)*2^k/(k * binomial(2*k,k)). - Amiram Eldar, Aug 19 2020
Equals 1/Product_{p prime} (1 - Kronecker(12,p)/p), where Kronecker(12,p) = 0 if p = 2 or 3, 1 if p == 1 or 11 (mod 12) or -1 if p == 5 or 7 (mod 12). - Amiram Eldar, Dec 17 2023
Equals A259830 - 2. - Hugo Pfoertner, Apr 06 2024
Equals (1/2)*2F1(1/2,1;3/2;3/4) [Krupnikov] - R. J. Mathar, Jun 11 2024
EXAMPLE
0.7603459963009463475310942548...
MATHEMATICA
RealDigits[Log[2 + Sqrt[3]]/Sqrt[3], 10, 89][[1]] (* Bruno Berselli, Dec 20 2011 *)
PROG
(PARI) log(sqrt(3)+2)/sqrt(3) \\ Charles R Greathouse IV, May 15 2019
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Oct 03 2011
STATUS
approved