A100199 Decimal expansion of Pi^2/(12*log(2)), inverse of Levy's constant.

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

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 27 2004

Keywords

• cons
• nonn

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

Examples

			1.1865691104156254528217229759472371205683565364720543359542542986528...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7, p. 54.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A086702, A089729, A072691, A002162, A174606.

Programs

Mathematica

RealDigits[Pi^2/(12*Log[2]), 10, 100][[1]] (* G. C. Greubel, Mar 23 2017 *)

PARI

Pi^2/log(4096) \\ Charles R Greathouse IV, Aug 04 2016

Formula

Equals 1/A089729 = log(A086702) = A174606/2.

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