

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
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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



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



KEYWORD

cofr,nonn


AUTHOR



STATUS

approved



