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A019712 Continued fraction expansion of tribonacci constant A058265. 4
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 (list; graph; refs; listen; history; text; internal format)
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
G. Xiao, Contfrac
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
KEYWORD
cofr,nonn
AUTHOR
Robert G. Wilson v, Dec 07 2000
STATUS
approved

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Last modified May 23 05:47 EDT 2024. Contains 372758 sequences. (Running on oeis4.)