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A039921
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Continued fraction expansion of w = 2*cos(Pi/7).
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6
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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
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OFFSET
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0,3
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COMMENTS
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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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A. M. Rucklidge & W. J. Rucklidge (preprint) 2002.
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LINKS
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FORMULA
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w satisfies w^3 - w^2 - 2w + 1 = 0 and so is algebraic.
The other two roots are 2*cos(3 Pi/7) and 2*cos(5 Pi/7); their continued fraction expansions also end in 20, 2, 3, 1, 6, 10, 5, 2, 2, 1, ... which is a(n) for n >= 3. - Greg Dresden, Jul 01 2018
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EXAMPLE
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w = 1.80193773580483825247220463901489010233183832426371430010712484639886...
Equals 1 + 1/(1 + 1/(4 + 1/(20 + 1/(2 + ...)))). - Harry J. Smith, May 31 2009
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MATHEMATICA
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ContinuedFraction[2*Cos[Pi/7], 100]
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PROG
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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])); } \\ Harry J. Smith, May 31 2009
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CROSSREFS
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KEYWORD
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cofr,nonn
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AUTHOR
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STATUS
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approved
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