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 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let P(k)/Q(k) denote the k-th 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 Gauss-Kuzmin distribution and the terms must occur in random order in the continued fraction sequence. - A.H.M. Smeets, Jun 26 2018 Named after the French mathematician Paul Lévy (1886 - 1971). - Amiram Eldar, Sep 25 2022 REFERENCES Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 59-65. Paul Lévy, Théorie de l'addition des variables aléatoires, 2nd. ed., Editions Jacques Gabay, 1954, chap. IX, pp. 316-320. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Paul Lévy, Sur le développement en fraction continue d'un nombre choisi au hasard, Compositio Mathematica, Vol. 3 (1936), pp. 286-303. Steven R. Finch, Khintchine's Constant. [Broken link] Steven R. Finch, Khintchine's Constant. [From the Wayback machine] Simon Plouffe, The Levy constant. [broken link] Eric Weisstein's World of Mathematics, Levy Constant. Eric Weisstein's World of Mathematics, Khinchin Constant. Eric Weisstein's World of Mathematics, Continued Fraction. Wikipedia, Lévy's constant. 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 := ComplexField(); [Exp((Pi(C))^2/(12*Log(2)))]; // G. C. Greubel, Nov 06 2017 CROSSREFS Cf. A002210. Sequence in context: A358139 A358654 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

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