%I #34 Jul 10 2024 15:03:45

%S 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,

%T 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,

%U 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

%N Continued fraction for zeta(3).

%H Harry J. Smith, <a href="/A013631/b013631.txt">Table of n, a(n) for n = 0..19999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AperysConstant.html">Apery's Constant</a>.

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.

%H <a href="/index/Z#zeta_function">Index entries for zeta function</a>.

%e zeta(3) = 1.2020569031595942... = 1 + 1/(4 + 1/(1 + 1/(18 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 20 2009

%t ContinuedFraction[ Zeta[3], 100]

%o (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

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

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

%K nonn,cofr,nice

%O 0,2

%A _N. J. A. Sloane_, John Morrison (John.Morrison(AT)armltd.co.uk)

%E Offset changed by _Andrew Howroyd_, Jul 10 2024