A078984 -id:A078984

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A013631

Continued fraction for zeta(3).

+10
31

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.

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

A078985

Denominators of continued fraction convergents to zeta(3).

+10
2

1, 4, 5, 94, 99, 193, 292, 1361, 1653, 16238, 147795, 311828, 459623, 771451, 1231074, 3233599, 23866267, 27099866, 50966133, 383862797, 4273456900, 4657319697, 8930776597, 13588096294, 49695065479, 63283161773, 429394036117

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

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

PROG

(PARI) a(n)=component(component(contfracpnqn(contfrac(zeta(3), n+1)), 1), 2)

CROSSREFS

Cf. A078984 (numerators), A013631 (continued fraction).