A013679 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

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.

EXAMPLE

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

MATHEMATICA

ContinuedFraction[ Pi^2/6, 100]

PROG

(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

CROSSREFS

Cf. A013661 (decimal expansion).

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

Sequence in context: A066978 A236187 A114566 * A096428 A091007 A180156

Adjacent sequences: A013676 A013677 A013678 * A013680 A013681 A013682

KEYWORD

nonn,cofr,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Andrew Howroyd, Jul 10 2024

STATUS

approved