A256425 Decimal expansion of the generalized Euler constant gamma(1,3).

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, 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, 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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.3, p. 32.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

D. H. Lehmer, Euler constants for arithmetic progressions, 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]

Formula

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

Equals -(psi(1/3) + log(3))/3 = (A047787 - A002391)/3. - Amiram Eldar, Jan 07 2024

Example

0.67780716378423221053372461245491438316931257963255620415268...

Mathematica

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

Prog

(PARI) Euler/3 + Pi*sqrt(3)/18 + log(3)/6 \\ Charles R Greathouse IV, Sep 08 2015
(PARI) -(psi(1/3) + log(3))/3 \\ Charles R Greathouse IV, Feb 03 2025

Crossrefs

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

Sequence in context: A349991 A351784 A008938 * A021600 A205867 A347417

Adjacent sequences: A256422 A256423 A256424 * A256426 A256427 A256428

Keyword

nonn,cons

Author

N. J. A. Sloane, Apr 09 2015

Status

approved