A239097 Decimal expansion of -(gamma-log(2))/2.

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

Offset

0,2

Comments

Decimal expansion of the generalized Euler constant -gamma(0,2).

Links

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

D. H. Lehmer, Euler constants for arithmetical progressions, Collection of articles in memory of Juriĭ Vladimirovič Linnik. Acta Arith. 27 (1975), 125--142. MR0369233 (51 #5468). See p. 128.

Formula

From Amiram Eldar, Jun 30 2020: (Start)

Equals Sum_{k>=1} zeta(2*k+1)/((2*k+1)*2^(2*k+1)).

Equals Sum_{k>=1} arctanh(1/(2*k)) - 1/(2*k). (End)

Example

.057965757829206224405360015687887068516670399210165827657456...

Mathematica

Join[{0}, RealDigits[(Log[2] - EulerGamma)/2, 10, 100][[1]]] (* G. C. Greubel, Aug 28 2018 *)

Prog

(PARI) (log(2)-Euler)/2 \\ Charles R Greathouse IV, Mar 25 2014
(Magma) SetDefaultRealField(RealField(100)); R:= RealField();
(Log(2) - EulerGamma(R))/2; // G. C. Greubel, Aug 28 2018

Crossrefs

Cf. A001620, A228725.

Sequence in context: A290151 A117031 A068456 * A153612 A276483 A021637

Adjacent sequences: A239094 A239095 A239096 * A239098 A239099 A239100

Keyword

nonn,cons

Author

N. J. A. Sloane, Mar 23 2014

Status

approved