%I #28 Jul 10 2024 15:03:41

%S 1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,15,1,3,6,1,1,2,1,1,1,2,2,3,1,

%T 3,1,1,5,1,2,2,1,1,6,27,20,3,97,105,1,1,1,1,1,45,2,8,19,1,4,1,1,3,1,2,

%U 1,1,1,5,1,1,2,3,6,1,1,1,2,1,5,1,1,2,9,5,3,2,1,1,1

%N Continued fraction for zeta(2) = Pi^2/6.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.

%D David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 23.

%H T. D. Noe, <a href="/A013679/b013679.txt">Table of n, a(n) for n = 0..9999</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%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 1.644934066848226436472415166... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...))))

%t ContinuedFraction[ Pi^2/6, 100]

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^2/6); for (n=1, 20000, write("b013679.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Apr 29 2009

%Y Cf. A013661 (decimal expansion).

%Y Cf. continued fractions for zeta(3)-zeta(20): A013631, A013680-A013696.

%K nonn,cofr,nice,easy

%O 0,5

%A _N. J. A. Sloane_

%E Offset changed by _Andrew Howroyd_, Jul 10 2024