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A100199 Decimal expansion of Pi^2/(12*log(2)), inverse of Levy's constant. 11
1, 1, 8, 6, 5, 6, 9, 1, 1, 0, 4, 1, 5, 6, 2, 5, 4, 5, 2, 8, 2, 1, 7, 2, 2, 9, 7, 5, 9, 4, 7, 2, 3, 7, 1, 2, 0, 5, 6, 8, 3, 5, 6, 5, 3, 6, 4, 7, 2, 0, 5, 4, 3, 3, 5, 9, 5, 4, 2, 5, 4, 2, 9, 8, 6, 5, 2, 8, 0, 9, 6, 3, 2, 0, 5, 6, 2, 5, 4, 4, 4, 3, 3, 0, 0, 3, 4, 8, 3, 0, 1, 1, 0, 8, 4, 8, 6, 8, 7, 5, 9, 4, 6, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
From A.H.M. Smeets, Jun 12 2018: (Start)
The denominator of the k-th convergent obtained from a continued fraction of a constant, the terms of the continued fraction satisfying the Gauss-Kuzmin distribution, will tend to exp(k*A100199).
Similarly, the error between the k-th convergent obtained from a continued fraction of a constant, and the constant itself will tend to exp(-2*k*A100199). (End)
The term "Lévy's constant" is sometimes used to refer to this constant (Wikipedia). - Bernard Schott, Sep 01 2022
LINKS
R. M. Corless, Continued Fractions and Chaos, Amer. Math. Monthly 99, 203-215, 1992.
Eric Weisstein's World of Mathematics, Khinchin-Levy Constant.
Eric Weisstein's World of Mathematics, Lévy Constant.
Wikipedia, Lévy's constant.
FORMULA
Equals 1/A089729 = log(A086702).
Equals ((Pi^2)/12)/log(2) = A072691 / A002162 = (Sum_{n>=1} ((-1)^(n+1))/n^2) / (Sum_{n>=1} ((-1)^(n+1))/n^1). - Terry D. Grant, Aug 03 2016
Equals (-1/log(2)) * Integral_{x=0..1} log(x)/(1+x) dx (from Corless, 1992). - Bernard Schott, Sep 01 2022
EXAMPLE
1.1865691104156254528217229759472371205683565364720543359542542986528...
MATHEMATICA
RealDigits[Pi^2/(12*Log[2]), 10, 100][[1]] (* G. C. Greubel, Mar 23 2017 *)
PROG
(PARI) Pi^2/log(4096) \\ Charles R Greathouse IV, Aug 04 2016
CROSSREFS
Sequence in context: A202258 A367409 A021540 * A161883 A248618 A197329
KEYWORD
cons,nonn
AUTHOR
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 27 2004
STATUS
approved

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Last modified June 14 20:28 EDT 2024. Contains 373401 sequences. (Running on oeis4.)