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

A. A. M. Cuyt and V. B. Petersen and B. Verdonk and H. Waadeland and W. B. Jones, Handbook of continued fractions for special functions (2008) Section 10.12

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,changed

Author

Eric W. Weisstein

Status

approved