

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
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OFFSET

1,3


COMMENTS

The denominator of the kth convergent obtained from a continued fraction of a constant, the terms of the continued fraction satisfying the GaussKuzmin distribution, will tend to exp(k*A100199).
Similarly, the error between the kth 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



FORMULA

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



CROSSREFS



KEYWORD



AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osakau.ac.jp), Dec 27 2004


STATUS

approved



