A002211 -id:A002211 - cp's OEIS frontend

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

Benoit Cloitre, Jul 28 2003

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.

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

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]

Cf. A002210, A002211.

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

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

A180848 Continued fraction for Khintchin^Khintchin.

Original entry on oeis.org

14, 5, 6, 2, 71, 1, 19, 1, 4, 1, 1, 1, 9, 1, 4, 1, 1, 464, 2, 4, 1, 1, 2, 3, 3, 2, 1, 1, 23, 2, 1, 1, 9, 4, 1, 1, 3, 11, 6, 1, 1, 1, 14, 2, 5, 8, 33, 7, 5, 2, 5, 5, 2, 3, 10, 3, 1, 1, 1, 8, 1, 2, 1, 7, 1, 1, 6, 1, 1, 11, 1, 7, 11, 5, 5, 1, 1, 7, 4, 1, 7, 1, 1, 4, 2, 24, 2, 16, 3, 1, 14, 3, 4, 2, 1, 2, 1

Offset: 1

Michel Lagneau, Sep 20 2010

Continued fraction for the constant A002210 raised to its own power.

			Khintchin^Khintchin = 14.194026774480... = 14 + 1/(5 + 1/(6 + 1/(2 + 1/(71 + 1/(1 + ...)))))

D. Shanks, Further evaluation of Khintchine's constant, Math. Comp., 14 (1960), 370-371.
D. Shanks and J. W. Wrench, Jr., Khintchine's constant, Amer. Math. Monthly, 66 (1959), 276-279.

Cf. A002210, A002211

ContinuedFraction[Khinchin^Khinchin, 100]

References converted to links - R. J. Mathar, Oct 06 2010

A224852 Positions of the incrementally largest terms in the continued fraction for Khinchin's constant.

Original entry on oeis.org

0, 3, 10, 15, 23, 104, 1701, 2445, 18995, 60037

Offset: 0

Eric W. Weisstein, Jul 22 2013

nonn

Same as A054870 except correctly indexed with [a_0; a_1, a_2, ...]

Eric Weisstein's World of Mathematics, Khinchin's Constant Continued Fraction

Cf. A054870 (= a(n) + 1).
Cf. A054866 (incrementally largest terms).
Cf. A002211 (continued fraction of Khinchin's constant).

Module[{nn=2500,k},k=ContinuedFraction[Khinchin,nn];DeleteDuplicates[Thread[{Range[nn],k}],GreaterEqual[#1[[2]],#2[[2]]]&]][[;;,1]]-1 (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Feb 28 2025 *)

a(n) = A054870(n) - 1.

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A086703 Continued fraction expansion of Levy's constant.

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A180848 Continued fraction for Khintchin^Khintchin.

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A224852 Positions of the incrementally largest terms in the continued fraction for Khinchin's constant.

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