A058297 Continued fraction for Wallis' number (A007493).

2, 10, 1, 1, 2, 1, 3, 1, 1, 12, 3, 5, 1, 1, 2, 1, 6, 1, 11, 4, 42, 1, 2, 1, 1, 1, 1, 1, 2, 1, 16, 1, 1, 1, 1, 6, 2, 5, 22, 6, 31, 2, 1, 4, 17, 2, 1, 5, 2, 4, 5, 2, 74, 45, 1, 24, 3, 1, 13, 1, 18, 2, 8, 1, 1, 5, 2, 1, 1, 2, 10, 1, 6, 6, 1, 1, 7, 21, 1, 1, 2, 2, 8, 3, 2, 2, 4, 9, 7, 4, 106, 3, 2, 1, 3, 2

Offset

0,1

Comments

The real solution to the equation x^3 - 2x - 5 = 0.

References

David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 27.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

2.09455148154232659148238654... = 2 + 1/(10 + 1/(1 + 1/(1 + 1/(2 + ...))))

Mathematica

ContinuedFraction[ 1/3*(135/2 - (3*Sqrt[1929])/2)^(1/3) + (1/2*(45 + Sqrt[1929]))^(1/3) / 3^(2/3), 100]

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=NULL; p=x^3 - 2*x - 5; rs=polroots(p); r=real(rs[1]); c=contfrac(r); for (n=1, 20001, write("b058297.txt", n-1, " ", c[n])); } \\ Harry J. Smith, May 03 2009
(PARI) contfrac(polrootsreal(x^3-2*x-5)[1]) \\ Charles R Greathouse IV, Apr 14 2014

Crossrefs

Cf. A007493.

Sequence in context: A189880 A189871 A096877 * A349623 A113160 A100078

Adjacent sequences: A058294 A058295 A058296 * A058298 A058299 A058300

Keyword

nonn,cofr

Author

Robert G. Wilson v, Dec 07 2000

Status

approved