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%I #44 Sep 04 2022 12:56:37
%S 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,
%T 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,
%U 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
%N Decimal expansion of Pi^2/(12*log(2)), inverse of Levy's constant.
%C From _A.H.M. Smeets_, Jun 12 2018: (Start)
%C 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).
%C 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)
%C The term "Lévy's constant" is sometimes used to refer to this constant (Wikipedia). - _Bernard Schott_, Sep 01 2022
%H G. C. Greubel, <a href="/A100199/b100199.txt">Table of n, a(n) for n = 1..10000</a>
%H R. M. Corless, <a href="https://www.jstor.org/stable/2325053">Continued Fractions and Chaos</a>, Amer. Math. Monthly 99, 203-215, 1992.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Khinchin-LevyConstant.html">Khinchin-Levy Constant</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LevyConstant.html">Lévy Constant</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lévy's_constant">Lévy's constant</a>.
%F Equals 1/A089729 = log(A086702).
%F 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
%F Equals (-1/log(2)) * Integral_{x=0..1} log(x)/(1+x) dx (from Corless, 1992). - _Bernard Schott_, Sep 01 2022
%e 1.1865691104156254528217229759472371205683565364720543359542542986528...
%t RealDigits[Pi^2/(12*Log[2]), 10, 100][[1]] (* _G. C. Greubel_, Mar 23 2017 *)
%o (PARI) Pi^2/log(4096) \\ _Charles R Greathouse IV_, Aug 04 2016
%Y Cf. A086702, A089729, A072691, A002162.
%K cons,nonn
%O 1,3
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 27 2004
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