A242000 Decimal expansion of delta = (1+alpha)/4, a constant appearing in Koecher's formula for Euler's gamma constant, where alpha is A065442, the Erdős-Borwein Constant.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 355.

Links

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

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 4.

Eric Weisstein's Mathworld, Erdős-Borwein Constant

Formula

alpha = sum_{n>=1} 1/(2^n-1) = A065442 = 1.606695...

delta = (1+alpha)/4 = 0.65167...

gamma = delta - (1/2)*sum_{k>=2} (((-1)^k/((k-1)*k*(k+1)))*floor(log(k)/log(2))) = A001620 = 0.5772... (Koecher's formula).

Example

0.6516737881038229409458253807977311451201449178764391089445...

Mathematica

alpha = 1/2 - QPolyGamma[0, 1, 2]/Log[2]; delta = (1+alpha)/4; RealDigits[delta, 10, 102] // First

Prog

(PARI) default(realprecision, 100); (1 + suminf(k=1, 1/(2^k - 1)))/4 \\ G. C. Greubel, Sep 06 2018

Crossrefs

Cf. A001620, A065442.

Sequence in context: A216582 A340543 A177824 * A238181 A197517 A102079

Adjacent sequences: A241997 A241998 A241999 * A242001 A242002 A242003

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 11 2014

Status

approved