A014538 Continued fraction for Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...

0, 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2, 1, 11, 1, 1, 1, 6, 1, 12, 1, 4, 7, 1, 1, 2, 5, 1, 5, 9, 1, 1, 1, 1, 33, 4, 1, 1, 3, 5, 3, 2, 1, 2, 1, 2, 1, 7, 6, 3, 1, 3, 3, 1, 1, 2, 1, 14, 1, 4, 4, 1, 2, 4, 1, 17, 4, 1, 14, 1, 1, 1, 12, 1

Offset

0,3

Comments

First 4,851,389,025 terms computed by Eric W. Weisstein, Aug 07 2013.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. J. Fee, Computation of Catalan's constant using Ramanujan's formula, in Proc. Internat. Symposium on Symbolic and Algebraic Computation (ISSAC '90). 1990, pp. 157-160.

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

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

C = 0.91596559417721901505... = 0 + 1/(1 + 1/(10 + 1/(1 + 1/(8 + ...))))

Mathematica

ContinuedFraction[Catalan, 100] (* G. C. Greubel, Aug 23 2018 *)

Prog

(PARI) default(realprecision, 100); contfrac(Catalan) \\ G. C. Greubel, Aug 23 2018
(Magma) R:= RealField(100); ContinuedFraction(Catalan(R)); // G. C. Greubel, Aug 23 2018

Crossrefs

Cf. A006752 (decimal expansion of Catalan's constant).

Cf. A099789 (high water marks), A099790 (positions of high water marks).

Cf. A006752, A104338, A153069, A153070, A054543, A118323. - Stuart Clary, Dec 17 2008

Sequence in context: A242553 A113513 A092030 * A160928 A105162 A010184

Adjacent sequences: A014535 A014536 A014537 * A014539 A014540 A014541

Keyword

nonn,cofr

Author

Eric W. Weisstein

Status

approved