login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087491 Decimal expansion of the Khinchin harmonic mean K_{-1}. 11
1, 7, 4, 5, 4, 0, 5, 6, 6, 2, 4, 0, 7, 3, 4, 6, 8, 6, 3, 4, 9, 4, 5, 9, 6, 3, 0, 9, 6, 8, 3, 6, 6, 1, 0, 6, 7, 2, 9, 4, 9, 3, 6, 6, 1, 8, 7, 7, 7, 9, 8, 4, 2, 5, 6, 5, 9, 5, 0, 1, 3, 7, 7, 3, 5, 1, 6, 0, 7, 8, 5, 7, 5, 2, 2, 0, 8, 7, 3, 4, 2, 5, 6, 5, 2, 0, 5, 7, 8, 8, 6, 4, 5, 6, 7, 8, 3, 2, 4, 2, 4, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Khinchin's constant is K_0 (A002210).

LINKS

Table of n, a(n) for n=1..102.

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

Eric Weisstein's World of Mathematics, Khinchin Harmonic Mean

Wikipedia, Khinchin's constant

FORMULA

Equals (Sum_{n>=1} -log2(1 - 1/(n+1)^2) * n^(-1))^(-1). - Jianing Song, Aug 08 2021

EXAMPLE

1.74540566...

MATHEMATICA

digits = 102; exactEnd = 1000; f[n_] = (1 - 1/(n + 1)^2)^(-1/n); s[n_] = Series[Log[f[n]], {n, Infinity, digits}] // Normal // N[#, digits] &; exactSum = Sum[Log[f[n]], {n, 1, exactEnd}] // N[#, digits] &; extraSum = Sum[s[n], {n, exactEnd + 1, Infinity}] // N[#, digits] &; A087491 = Log[2]/(exactSum + extraSum) // RealDigits // First  (* Jean-François Alcover, Feb 06 2013 *)

RealDigits[Log[2]/NSum[Log[(1 - 1/(n + 1)^2)^(-1/n)], {n, Infinity}, NSumTerms -> 10^4, WorkingPrecision -> 250, PrecisionGoal -> 110]][[1, ;; 100]] (* Eric W. Weisstein, Dec 10 2017 *)

CROSSREFS

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

Sequence in context: A180078 A019685 A208899 * A019899 A085662 A155684

Adjacent sequences:  A087488 A087489 A087490 * A087492 A087493 A087494

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Sep 09 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 4 19:40 EST 2021. Contains 349526 sequences. (Running on oeis4.)