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A228725 Decimal expansion of the generalized Euler constant gamma(1,2). 18
6, 3, 5, 1, 8, 1, 4, 2, 2, 7, 3, 0, 7, 3, 9, 0, 8, 5, 0, 1, 1, 8, 7, 2, 1, 0, 5, 7, 7, 0, 2, 8, 9, 4, 9, 9, 5, 5, 8, 8, 2, 9, 7, 3, 5, 1, 5, 0, 0, 8, 9, 4, 2, 6, 4, 6, 3, 2, 2, 3, 6, 2, 2, 1, 8, 9, 1, 3, 0, 6, 7, 4, 3, 7, 3, 6, 7, 9, 6, 9, 3, 2, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The complement (A239097) is gamma(0,2) = lim_{x -> infinity} (Sum_{0<n<=x, n even} (1/n - log(x)/2) = (A001620 - A002162)/2 = -0.05796575... - R. J. Mathar, Sep 06 2013

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

J. C. Lagarias, Euler's constant: Euler's work and modern developments, arXiv:1303.1856 [math.NT], 2013. See Section 3.8.

D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) 125-142

FORMULA

Equals lim_{x -> infinity} (Sum_{0<n<=x, n odd} 1/n - log(x)/2).

Equals (A001620 + A002162)/2.

EXAMPLE

.63518142273073908501187210577028949955882973515008942646322...

MAPLE

(gamma+log(2))/2 ; evalf(%) ;

MATHEMATICA

RealDigits[(EulerGamma+Log[2])/2, 10, 120][[1]] (* Harvey P. Dale, Dec 26 2013 *)

PROG

(PARI) (Euler+log(2))/2 \\ Charles R Greathouse IV, Jul 21 2015

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField();

(EulerGamma + Log(2))/2; // G. C. Greubel, Aug 27 2018

CROSSREFS

Cf. A001620, A002162, A239097.

Sequence in context: A195471 A305187 A065418 * A286982 A153595 A195482

Adjacent sequences:  A228722 A228723 A228724 * A228726 A228727 A228728

KEYWORD

nonn,cons

AUTHOR

R. J. Mathar, Aug 31 2013

STATUS

approved

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Last modified December 14 18:21 EST 2018. Contains 318106 sequences. (Running on oeis4.)