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A058297 Continued fraction for Wallis' number (A007493). 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A113160 A100078 A051242

Adjacent sequences:  A058294 A058295 A058296 * A058298 A058299 A058300

KEYWORD

nonn,cofr

AUTHOR

Robert G. Wilson v, Dec 07 2000

STATUS

approved

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Last modified June 24 05:39 EDT 2019. Contains 324318 sequences. (Running on oeis4.)