A013680 - OEIS

%I #30 Jul 09 2024 20:34:27

%S 1,12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,1,1,1,1,3,2,4,2,2,22,1,

%T 13,5,1,4,2,1,3,1,1,1,6,11,40,1,7,5,2,4,1,2,3,14,9,1,33,78,1,12,4,1,2,

%U 551,1,1,1,1,1,1,2,1,9,2,7,3,1,3,2,15,1,1,2,2

%N Continued fraction for zeta(4).

%H T. D. Noe, <a href="/A013680/b013680.txt">Table of n, a(n) for n = 0..9999</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(4) = 1 + 1/(12 + 1/(6 + 1/(1 + 1/(3 + ...)))). - _Harry J. Smith_, Apr 29 2009

%t ContinuedFraction[Zeta[4],80] (* _Harvey P. Dale_, Oct 13 2013 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^4/90); for (n=1, 20000, write("b013680.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Apr 29 2009

%Y Cf. A013662 (zeta(4)). - _Harry J. Smith_, Apr 29 2009

%Y Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013681-A013696.

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_

%E Offset changed by _Andrew Howroyd_, Jul 09 2024