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Continued fraction for 2*zeta(3).
6

%I #22 Jul 10 2024 14:54:56

%S 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,

%T 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,

%U 1,8,2,1,9,2,1,11,1,3,3,4,1,28,6,1,28,1,15,1,1,1,2

%N Continued fraction for 2*zeta(3).

%H Harry J. Smith, <a href="/A060804/b060804.txt">Table of n, a(n) for n = 0..19999</a>

%H Y. V. Nesterenko, <a href="https://web.archive.org/web/20020608061629/http://www.ufr-mi.u-bordeaux.fr:80/~brisebar/GT/9899/Nest/nest29avril.html">Zeta(3) and recurrence relations.</a>

%H Y. V. Nesterenko, <a href="https://doi.org/10.4213/mzm1785">A few remarks on zeta(3)</a>, Mathematical Notes, 59 (No. 6, 1996), 625-636.

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

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

%o (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

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

%Y Cf. A152648 (decimal expansion).

%K nonn,cofr

%O 0,1

%A _N. J. A. Sloane_, Apr 29 2001

%E Offset changed by _Andrew Howroyd_, Jul 10 2024