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

1,3

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

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.

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

Cf. A086702, A089729, A072691, A002162.

Sequence in context: A202258 A367409 A021540 * A161883 A248618 A197329

Adjacent sequences: A100196 A100197 A100198 * A100200 A100201 A100202

Keyword

cons,nonn

Author

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

Status

approved