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A086703 Continued fraction expansion of Levy's constant. 1

%I #27 Apr 19 2019 03:29:37

%S 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,

%T 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,

%U 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

%N Continued fraction expansion of Levy's constant.

%C 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.

%D Paul Lévy, Théorie de l'addition des variables aléatoires, 2nd. ed., Editions Jacques Gabay, chap IX, pp. 316-320.

%H Patrick McKinley, <a href="/A086703/b086703.txt">Table of n, a(n) for n = 0..20298</a> (computed using bc with scale of 20806, Mar 02 2013)

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/khntchn/khntchn.html">Khintchine's Constant</a> [Broken link]

%H Steven R. Finch, <a href="http://web.archive.org/web/20011108021950/http://www.mathsoft.com/asolve/constant/khntchn/khntchn.html">Khintchine's Constant</a> [From the Wayback machine]

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

%o (PARI) contfrac(exp(Pi^2/12/log(2))) \\ _Charles R Greathouse IV_, Mar 06 2013

%Y Cf. A002210, A002211.

%K cofr,nonn

%O 0,1

%A _Benoit Cloitre_, Jul 28 2003

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