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Search: id:A019712
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| A019712 |
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Continued fraction expansion of tribonacci constant. |
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+0
2
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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The only real root of the equation x^3 - x^2 - x - 1 = 0.
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REFERENCES
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David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 23.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
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EXAMPLE
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1.839286755214161132551852564... = 1 + 1/(1 + 1/(5 + 1/(4 + 1/(2 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 30 2009]
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MATHEMATICA
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ContinuedFraction[ 1/3 + 1/3*(19 - 3*Sqrt[33])^(1/3) + 1/3*(19 + 3*Sqrt[33])^(1/3), 100]
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PROGRAM
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(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])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 30 2009]
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CROSSREFS
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Cf. A058265 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 30 2009]
Sequence in context: A074825 A094778 A097960 this_sequence A020799 A073743 A021652
Adjacent sequences: A019709 A019710 A019711 this_sequence A019713 A019714 A019715
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KEYWORD
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cofr,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 07 2000
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