A013631 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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.

EXAMPLE

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

MATHEMATICA

ContinuedFraction[ Zeta[3], 100]

PROG

(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

CROSSREFS

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

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

Sequence in context: A052179 A171589 A126331 * A331651 A113355 A201201

Adjacent sequences: A013628 A013629 A013630 * A013632 A013633 A013634

KEYWORD

nonn,cofr,nice

AUTHOR

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

EXTENSIONS

Offset changed by Andrew Howroyd, Jul 10 2024

STATUS

approved