A256425 - OEIS

%I #26 Jan 07 2024 01:55:14

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

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

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

%N Decimal expansion of the generalized Euler constant gamma(1,3).

%H G. C. Greubel, <a href="/A256425/b256425.txt">Table of n, a(n) for n = 0..5000</a>

%H D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa27/aa27121.pdf">Euler constants for arithmetic progressions</a>, Acta Arith. 27 (1975), 125-142. [gamma=A001620, gamma(0,2)=A239097, gamma(1,2)=A228725, N_k=A007947, gamma(1,3)=A256425, the present sequence]

%F Equals gamma/3+Pi*sqrt(3)/18+log(3)/6.

%F Equals -(psi(1/3) + log(3))/3 = (A047787 - A002391)/3. - _Amiram Eldar_, Jan 07 2024

%e 0.67780716378423221053372461245491438316931257963255620415268...

%t RealDigits[EulerGamma/3 + Pi*Sqrt[3]/18 + Log[3]/6, 10, 50][[1]] (* _G. C. Greubel_, Jun 08 2017 *)

%o (PARI) Euler/3 + Pi*sqrt(3)/18 + log(3)/6 \\ _Charles R Greathouse IV_, Sep 08 2015

%Y Cf. A001620, A002391, A007947, A047787, A228725, A239097.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_, Apr 09 2015