

A086702


Decimal expansion of Lévy's constant.


14



3, 2, 7, 5, 8, 2, 2, 9, 1, 8, 7, 2, 1, 8, 1, 1, 1, 5, 9, 7, 8, 7, 6, 8, 1, 8, 8, 2, 4, 5, 3, 8, 4, 3, 8, 6, 3, 6, 0, 8, 4, 7, 5, 5, 2, 5, 9, 8, 2, 3, 7, 4, 1, 4, 9, 4, 0, 5, 1, 9, 8, 9, 2, 4, 1, 9, 0, 7, 2, 3, 2, 1, 5, 6, 4, 4, 9, 6, 0, 3, 5, 5, 1, 8, 1, 2, 7, 7, 5, 4, 0, 4, 7, 9, 1, 7, 4, 5, 2, 9, 4, 9, 2, 6, 9
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OFFSET

1,1


COMMENTS

Let P(k)/Q(k) denote the kth convergent of x. Then for almost all irrational values of x, lim_{k>inf} Q(k)^(1/k) = L. [edited by Jared Kish, Oct 17 2014; edited by A.H.M. Smeets, Jun 26 2018]
The conditions for x, such that lim_{k>inf} Q(k)^(1/k) = L, are that the terms occurring in the continued fraction for the value of x must satisfy the GaussKuzmin distribution and the terms must occur in random order in the continued fraction sequence.  A.H.M. Smeets, Jun 26 2018


REFERENCES

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 5965
Paul Lévy, Théorie de l'addition des variables aléatoires, 2nd. ed., Editions Jacques Gabay, chap IX, pp. 316320.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Steven R. Finch, Khintchine's Constant [Broken link]
Steven R. Finch, Khintchine's Constant [From the Wayback machine]
Simon Plouffe, The Levy constant
Eric Weisstein's World of Mathematics, Levy Constant
Eric Weisstein's World of Mathematics, Khinchin Constant
Eric Weisstein's World of Mathematics, Continued Fraction


FORMULA

L = exp(Pi^2/(12*log(2))).


EXAMPLE

3.27582291872181115978768...


MATHEMATICA

RealDigits[E^(Pi^2/Log[4096]), 10, 111][[1]] (* Robert G. Wilson v, May 19 2004 *)


PROG

(PARI) exp(Pi^2/12/log(2)) \\ Michel Marcus, Apr 18 2015
(MAGMA) C<i> := ComplexField(); [Exp((Pi(C))^2/(12*Log(2)))]; // G. C. Greubel, Nov 06 2017


CROSSREFS

Cf. A002210.
Sequence in context: A307544 A126314 A200714 * A156140 A324556 A069888
Adjacent sequences: A086699 A086700 A086701 * A086703 A086704 A086705


KEYWORD

cons,nonn


AUTHOR

Benoit Cloitre, Jul 28 2003


EXTENSIONS

Offset corrected by R. J. Mathar, Feb 05 2009


STATUS

approved



