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A010123
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Continued fraction for sqrt(14).
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4
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3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 56. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 22 2009]
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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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FORMULA
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a(n)=(1/6)*{-5*(n mod 4)+4*[(n+1) mod 4]+[(n+2) mod 4]+10*[(n+3) mod 4]}-3*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Jun 11 2009]
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EXAMPLE
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3.741657386773941385583748732... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(6 + ...)))) [From Harry J. Smith, Jun 02 2009]
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MATHEMATICA
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ContinuedFraction[Sqrt[14], 300] (*From Vladimir Joseph Stephan Orlovsky, Mar 05 2011*)
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(14)); for (n=0, 20000, write("b010123.txt", n, " ", x[n+1])); } [From Harry J. Smith, Jun 02 2009]
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CROSSREFS
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Cf. A010471 Decimal expansion. [From Harry J. Smith, Jun 02 2009]
Sequence in context: A135261 A102774 A131918 * A039620 A008296 A140185
Adjacent sequences: A010120 A010121 A010122 * A010124 A010125 A010126
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KEYWORD
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nonn,cofr
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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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