A196530 Decimal expansion of log(2+sqrt(3))/sqrt(3).

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

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.

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).

Index entries for transcendental numbers.

Formula

Equals A065918/A002194.

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

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

Cf. A065918, A002194, A110161.

Sequence in context: A198677 A154017 A100222 * A154850 A011236 A343280

Adjacent sequences: A196527 A196528 A196529 * A196531 A196532 A196533

Keyword

nonn,cons,easy

Author

R. J. Mathar, Oct 03 2011

Status

approved