A019712 Continued fraction expansion of tribonacci constant A058265.

1, 1, 5, 4, 2, 305, 1, 8, 2, 1, 4, 6, 14, 3, 1, 13, 5, 1, 7, 23, 1, 16, 4, 1, 1, 1, 1, 1, 2, 17, 1, 3, 1, 1, 1, 29, 1, 6, 1, 3, 1, 1, 1, 1, 3, 2, 5, 1, 63, 2, 1, 2, 5, 1, 4, 11, 2, 2, 1, 1, 1, 1, 1, 2, 1, 9, 3, 3, 18, 1, 38, 2, 4, 1, 20, 3, 1, 1, 1, 5, 2, 2, 1, 1, 1, 44, 6, 3, 9, 1, 1, 1, 1, 3, 3, 1, 6

Offset: 0

Author

Robert G. Wilson v, Dec 07 2000

Keywords

• cofr
• nonn

Comments

The only real root of the equation x^3 - x^2 - x - 1 = 0.

Examples

			1.839286755214161132551852564... = 1 + 1/(1 + 1/(5 + 1/(4 + 1/(2 + ...)))). - _Harry J. Smith_, May 30 2009
		

References

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

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. A058265 (decimal expansion), A319428/A319429 (convergents).

Programs

Mathematica

ContinuedFraction[ 1/3 + 1/3*(19 - 3*Sqrt[33])^(1/3) + 1/3*(19 + 3*Sqrt[33])^(1/3), 100]

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(solve(x=1, 2, x^3 - x^2 - x - 1)); for (n=0, 20000, write("b019712.txt", n, " ", x[n+1])); } \\ Harry J. Smith, May 30 2009