A013679 Continued fraction for zeta(2) = Pi^2/6.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• nice
• easy

Examples

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

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..9999
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• G. Xiao, Contfrac
• Index entries for continued fractions for constants
• Index entries for zeta function.

Crossrefs

Cf. A013661 (decimal expansion).

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

Programs

Mathematica

ContinuedFraction[ Pi^2/6, 100]

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

Extensions

Offset changed by Andrew Howroyd, Jul 10 2024