A060804 Continued fraction for 2*zeta(3).

2, 2, 2, 9, 3, 10, 1, 4, 18, 1, 3, 5, 3, 1, 3, 3, 1, 1, 5, 3, 8, 1, 2, 1, 62, 1, 1, 1, 3, 2, 2, 1, 1, 5, 3, 1, 8, 2, 2, 34, 7, 1, 1, 5, 1, 2, 3, 3, 14, 9, 214, 11, 8, 23, 1, 8, 2, 10, 2, 2, 2, 1, 1, 6, 1, 8, 2, 1, 9, 2, 1, 11, 1, 3, 3, 4, 1, 28, 6, 1, 28, 1, 15, 1, 1, 1, 2

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..19999

Y. V. Nesterenko, Zeta(3) and recurrence relations, Séminaire de Théorie Analytique des Nombres et Problèmes Diophantiens, 1999.

Y. V. Nesterenko, A few remarks on zeta(3), Mathematical Notes, 59 (No. 6, 1996), 625-636.

Example

2.404113806319188570799476323... = 2 + 1/(2 + 1/(2 + 1/(9 + 1/(3 + ...)))). - Harry J. Smith, Jul 12 2009

Maple

Digits := 100: t1 := evalf(2*Zeta(3)); convert(t1, confrac);

Mathematica

ContinuedFraction[2 Zeta[3], 90] (* Harvey P. Dale, Apr 25 2025 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(2*zeta(3)); for (n=1, 20000, write("b060804.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Jul 12 2009
(Python)
from sympy.ntheory.continued_fraction import continued_fraction_iterator
from sympy import zeta
def A060804(): yield from continued_fraction_iterator(2*zeta(3)) # Aidan Chen, Jan 24 2026

Crossrefs

Cf. A060805, A060806, A060807, A060808 (convergents).

Cf. A152648 (decimal expansion).

Sequence in context: A138056 A340080 A022459 * A086364 A260662 A228044

Adjacent sequences: A060801 A060802 A060803 * A060805 A060806 A060807

Keyword

nonn,cofr

Author

N. J. A. Sloane, Apr 29 2001

Extensions

Offset changed by Andrew Howroyd, Jul 10 2024

Status

approved