A086703 Continued fraction expansion of Levy's constant.

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

Cf. A002210, A002211.

Sequence in context: A127197 A114231 A079075 * A242849 A072917 A319861

Adjacent sequences: A086700 A086701 A086702 * A086704 A086705 A086706

Keyword

cofr,nonn

Author

Benoit Cloitre, Jul 28 2003

Status

approved