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A256783 Decimal expansion of the generalized Euler constant gamma(1,12). 9
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 (list; constant; graph; refs; listen; history; text; internal format)
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)).

Sum_{n>=0} (1/(12n+1) - 1/12*log((12n+13)/(12n+1))).

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

Sequence in context: A107671 A271174 A216891 * A154538 A154166 A010521

Adjacent sequences:  A256780 A256781 A256782 * A256784 A256785 A256786

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Apr 10 2015

STATUS

approved

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Last modified December 18 23:46 EST 2018. Contains 318245 sequences. (Running on oeis4.)