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

Author

Benoit Cloitre, Jul 28 2003

Keywords

• cofr
• nonn

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]

Crossrefs

Cf. A002210, A002211.

Programs

PARI

contfrac(exp(Pi^2/12/log(2))) \\ Charles R Greathouse IV, Mar 06 2013

Formula

L = exp(Pi^2/12/log(2)) = 3.27582291872181115978768...