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

0,3

Comments

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A058265 (decimal expansion).

Sequence in context: A175838 A347272 A097960 * A020799 A199432 A073743

Adjacent sequences: A019709 A019710 A019711 * A019713 A019714 A019715

Keyword

cofr,nonn

Author

Robert G. Wilson v, Dec 07 2000

Status

approved