A256783 Decimal expansion of the generalized Euler constant gamma(1,12).

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

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

Cf. A001620 (EulerGamma), A016635, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

Sequence in context: A271174 A216891 A349454 * A154538 A154166 A338612

Adjacent sequences: A256780 A256781 A256782 * A256784 A256785 A256786

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 10 2015

Status

approved