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

Author

Robert G. Wilson v, Dec 07 2000

Keywords

• nonn
• cofr

Comments

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

Examples

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

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

Crossrefs

Cf. A007493.

Programs

Mathematica

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

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