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Search: id:A039921
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| A039921 |
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Continued fraction expansion of w=2*cos(pi/7). |
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+0
3
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| 1, 1, 4, 20, 2, 3, 1, 6, 10, 5, 2, 2, 1, 2, 2, 1, 18, 1, 1, 3, 2, 1, 2, 1, 2, 1, 39, 2, 1, 1, 1, 13, 1, 2, 1, 30, 1, 1, 1, 3, 2, 5, 4, 1, 5, 1, 5, 1, 2, 1, 1, 94, 6, 2, 19, 11, 1, 60, 1, 1, 50, 2, 1, 1, 8, 53, 1, 3, 1, 6, 3, 2, 1, 5, 1, 1, 3, 4, 636, 1, 2, 1, 3, 3, 7, 9, 1, 2, 10, 3, 1, 22, 1, 119, 3
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Arises in the approximation of 14-fold quasipatterns by 14 Fourier modes.
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REFERENCES
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S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
A. M. Rucklidge & W. J. Rucklidge (preprint) 2002.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
Alastair Rucklidge, Home page
G. Xiao, Contfrac
Index entries for continued fractions for constants
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FORMULA
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w satisfies w^3 - w^2 - 2w + 1 = 0 and so is algebraic.
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EXAMPLE
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w = 1.801937735804838252472204639014890102331838324263714300107124846398864840...
1.80193773580483825247220463... = 1 + 1/(1 + 1/(4 + 1/(20 + 1/(2 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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MATHEMATICA
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ContinuedFraction[2*Cos[Pi/7], 100]
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PROGRAM
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(2*cos(Pi/7)); for (n=0, 20000, write("b039921.txt", n, " ", x[n+1])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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CROSSREFS
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Cf. A160389 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
Sequence in context: A023994 A002813 A104159 this_sequence A081852 A050017 A125514
Adjacent sequences: A039918 A039919 A039920 this_sequence A039922 A039923 A039924
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KEYWORD
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cofr,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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