A114610 Decimal expansion of Sum_{k=-infinity..+infinity} log(2)/(2^(-k/2) + 2^(k/2))^2.

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

Offset

0,12

Comments

Differs from 1 by 4.9*10^-11.

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's World of Mathematics, Almost Integer

Example

1.00000000004885109041382...

Mathematica

almostOne = Log[2]/4 + 2*Log[2]*NSum[1/(2^(-k/2) + 2^(k/2))^2, {k, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 100]; RealDigits[almostOne, 10, 102] // First (* Jean-François Alcover, Feb 07 2013 *)
RealDigits[Re[2 - Log[2]/4 - 2*(QPolyGamma[1, -((I*Pi)/Log[2]), Sqrt[2]] + QPolyGamma[1, (I*Pi)/Log[2], Sqrt[2]])/Log[2]], 10, 100][[1]] (* Vaclav Kotesovec, Aug 17 2015 *)

Crossrefs

Sequence in context: A064927 A343881 A227896 * A200390 A137209 A329506

Adjacent sequences: A114607 A114608 A114609 * A114611 A114612 A114613

Keyword

nonn,cons

Author

Eric W. Weisstein, Dec 15 2005

Status

approved