A060807 -id:A060807 - cp's OEIS frontend

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

N. J. A. Sloane, Apr 29 2001

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

Harry J. Smith, Table of n, a(n) for n = 0..19999
Y. V. Nesterenko, Zeta(3) and recurrence relations.
Y. V. Nesterenko, A few remarks on zeta(3), Mathematical Notes, 59 (No. 6, 1996), 625-636.

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

Cf. A152648 (decimal expansion).

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

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

{ 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

Offset changed by Andrew Howroyd, Jul 10 2024

A060805 Numerators of special continued fraction for 2*zeta(3).

Original entry on oeis.org

2, 1, 2, 1, 4, 2, 6, 4, 9, 6, 12, 9, 16, 12, 20, 16, 25, 20, 30, 25, 36, 30, 42, 36, 49, 42, 56, 49, 64, 56, 72, 64, 81, 72, 90, 81, 100, 90, 110, 100, 121, 110, 132, 121, 144, 132, 156, 144, 169, 156, 182, 169, 196, 182, 210, 196, 225, 210, 240, 225, 256, 240, 272, 256

Offset: 1

N. J. A. Sloane, Apr 29 2001

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

Y. V. Nesterenko, Zeta(3) and recurrence relations.
Yu. V. Nesterenko, A few remarks on zeta(3), Math. Notes 59 (1996) 625-636. [From _R. J. Mathar_, Jul 31 2010]
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

Cf. A060804, A060806, A060807, A060808, A008733.

Cf. A152648 (2*zeta(3)).

A060805 := proc(n) local nshf,k ; if n <= 2 then op(n,[2,1]) ; else nshf := n-1 ; k := floor(nshf/4) ; if nshf mod 4 = 1 then k*(k+1) ; elif nshf mod 4 = 0 then (k+1)^2 ; elif nshf mod 4 = 2 then (k+1)*(k+2) ; else (k+1)^2 ; end if; end if; end proc: seq(A060805(n),n=1..80) ; # R. J. Mathar, Jul 31 2010

Join[{2, 1}, LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {2, 1, 4, 2, 6, 4, 9}, 100]] (* Jean-François Alcover, Apr 01 2020 *)

a(n) = A008733(n-1), n>2. - R. J. Mathar, Jul 31 2010

More terms from R. J. Mathar, Jul 31 2010

A060808 Denominators of ordinary continued fraction convergents for 2*zeta(3).

Original entry on oeis.org

1, 2, 5, 47, 146, 1507, 1653, 8119, 147795, 155914, 615537, 3233599, 10316334, 13549933, 50966133, 166448332, 217414465, 383862797, 2136728450, 6794048147, 56489113626, 63283161773, 183055437172, 246338598945, 15456048571762

Offset: 0

N. J. A. Sloane, Apr 29 2001

			2, 5/2, 12/5, 113/47, 351/146, 3623/1507, 3974/1653, ...

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

Y. V. Nesterenko, Zeta(3) and recurrence relations.

Cf. A060804, A060805, A060806, A060807 (numerators).

Digits := 100: t1 := evalf(2*Zeta(3)); cfrac(t1,l1,l2); l1;

More terms from Vladeta Jovovic, Apr 29 2001

Offset changed by Andrew Howroyd, Jul 10 2024

cp's OEIS Frontend

A060804 Continued fraction for 2*zeta(3).

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A060805 Numerators of special continued fraction for 2*zeta(3).

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A060808 Denominators of ordinary continued fraction convergents for 2*zeta(3).

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