A013631 Continued fraction for zeta(3).

1, 4, 1, 18, 1, 1, 1, 4, 1, 9, 9, 2, 1, 1, 1, 2, 7, 1, 1, 7, 11, 1, 1, 1, 3, 1, 6, 1, 30, 1, 4, 1, 1, 4, 1, 3, 1, 2, 7, 1, 3, 1, 2, 2, 1, 16, 1, 1, 3, 3, 1, 2, 2, 1, 6, 1, 1, 1, 6, 1, 1, 4, 428, 5, 1, 1, 3, 1, 1, 11, 2, 4, 4, 5, 4, 1, 5, 14, 1, 3, 1, 2, 19, 1, 2, 5, 1, 7, 1, 1, 1, 1, 1, 57, 3, 2, 14, 2

Offset: 0

Author

N. J. A. Sloane, John Morrison (John.Morrison(AT)armltd.co.uk)

Keywords

• nonn
• cofr
• nice

Examples

			zeta(3) = 1.2020569031595942... = 1 + 1/(4 + 1/(1 + 1/(18 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 20 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..19999
• Eric Weisstein's World of Mathematics, Apery's Constant.
• G. Xiao, Contfrac.
• Index entries for continued fractions for constants.
• Index entries for zeta function.

Crossrefs

Cf. A002117 (decimal expansion), A078984, A078985 (convergents).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013680-A013696.

Programs

Mathematica

ContinuedFraction[ Zeta[3], 100]

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(zeta(3)); for (n=1, 20000, write("b013631.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 20 2009

Extensions

Offset changed by Andrew Howroyd, Jul 10 2024