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A086703
Continued fraction expansion of Levy's constant.
1
3, 3, 1, 1, 1, 2, 29, 1, 130, 1, 12, 3, 8, 2, 4, 1, 3, 55, 2, 4, 2, 2, 1, 797, 1, 1, 6, 2, 4, 1, 13, 2, 1, 6, 1, 4, 2, 1, 9, 3, 2, 2, 2, 2, 4, 1, 2, 5, 1, 1, 1, 6, 2, 2, 1, 32, 1, 2, 1, 3, 2, 1, 15, 3, 1, 1, 1, 2, 1, 1, 105, 1, 79, 1, 4, 2, 3, 11, 1, 6, 1, 7, 2, 1, 3, 1, 9, 1, 4, 9, 1, 1, 3, 1, 1, 15, 1, 6
OFFSET
0,1
COMMENTS
Let P(k)/Q(k) denote the k-th convergent of x, then for almost all real values 0 < x < 1 we have limit k -> infinity Q(k)^(1/k) = L.
REFERENCES
Paul Lévy, Théorie de l'addition des variables aléatoires, 2nd. ed., Editions Jacques Gabay, chap IX, pp. 316-320.
LINKS
Patrick McKinley, Table of n, a(n) for n = 0..20298 (computed using bc with scale of 20806, Mar 02 2013)
Steven R. Finch, Khintchine's Constant [Broken link]
Steven R. Finch, Khintchine's Constant [From the Wayback machine]
FORMULA
L = exp(Pi^2/12/log(2)) = 3.27582291872181115978768...
PROG
(PARI) contfrac(exp(Pi^2/12/log(2))) \\ Charles R Greathouse IV, Mar 06 2013
CROSSREFS
Sequence in context: A127197 A114231 A079075 * A242849 A072917 A319861
KEYWORD
cofr,nonn
AUTHOR
Benoit Cloitre, Jul 28 2003
STATUS
approved