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

Author

Jean-François Alcover, Aug 11 2014

Keywords

• nonn
• cons
• easy

Examples

			0.6516737881038229409458253807977311451201449178764391089445...
		

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

Crossrefs

Cf. A001620, A065442.

Programs

Mathematica

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

PARI

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

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).