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A010173
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Continued fraction for sqrt(107).
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4
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10, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1, 9, 1, 2, 20, 2, 1
(list;
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refs;
listen;
history;
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OFFSET
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0,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..999
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
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FORMULA
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a(n) = (1/18)*(-47*(n mod 6) + 4*((n+1) mod 6) + 31*((n+2) mod 6) - 17*((n+3) mod 6) + 10*((n+4) mod 6) + 61*((n+5) mod 6)) - 10*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Jul 24 2009
G.f.: (-10*x^6 - 2*x^5 - x^4 - 9*x^3 - x^2 - 2*x - 10)/(x^6 - 1). - Chai Wah Wu, Oct 02 2021
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MATHEMATICA
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ContinuedFraction[Sqrt[107], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2011 *)
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PROG
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(Python)
from sympy import sqrt
from sympy.ntheory.continued_fraction import continued_fraction_iterator
def aupton(terms):
gen = continued_fraction_iterator(sqrt(107))
return [next(gen) for i in range(terms)]
print(aupton(82)) # Michael S. Branicky, Oct 02 2021
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CROSSREFS
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Cf. A177935 (decimal expansion), A041192/A041193 (convergents).
Sequence in context: A040097 A010174 A073755 * A357339 A259712 A343103
Adjacent sequences: A010170 A010171 A010172 * A010174 A010175 A010176
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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