A087492 Decimal expansion of Khinchin mean K_{-2}.

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

Offset

1,2

Comments

Khinchin's constant is K_0.

Links

Table of n, a(n) for n=1..103.

Eric Weisstein's World of Mathematics, Khinchin's Constant

Example

1.45034032...

Mathematica

digits = 102; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^2*Log[2])); s[n_] = Series[f[n] , {n, Infinity, digits}] // Normal // N[#, digits]&; exactSum = Sum[f[n] , {n, 1, exactEnd}] // N[#, digits]&; extraSum = Sum[s[n] , {n, exactEnd + 1, Infinity}] // N[#, digits]&; A087492 = 1/Sqrt[exactSum + extraSum] // RealDigits // First (* Jean-François Alcover, Feb 06 2013 *)

Crossrefs

Cf. A002210, A087491, A087492, A087493, A087494, A087495, A087496, A087497, A087498, A087499, A087500.

Sequence in context: A270914 A048837 A353450 * A366362 A199967 A021226

Adjacent sequences: A087489 A087490 A087491 * A087493 A087494 A087495

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 09 2003

Extensions

More terms from Jean-François Alcover, Feb 06 2013

Status

approved