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

Author

Eric W. Weisstein

Keywords

• nonn
• cofr

Comments

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

Examples

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

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

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

Programs

Magma

R:= RealField(100); ContinuedFraction(Catalan(R)); // G. C. Greubel, Aug 23 2018

Mathematica

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

PARI

default(realprecision, 100); contfrac(Catalan) \\ G. C. Greubel, Aug 23 2018