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A040007
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Continued fraction for sqrt(11).
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3
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3, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Eventual period is (3,6). - Zak Seidov, Mar 05 2011
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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
Index entries for linear recurrences with constant coefficients, signature (0, 1).
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FORMULA
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a(n) = (1/2)(9 + 3*(-1)^n) - 3*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 11 2009
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EXAMPLE
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3.316624790355399849114932736... = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009
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MAPLE
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Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
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MATHEMATICA
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ContinuedFraction[Sqrt[11], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(11)); for (n=0, 20000, write("b040007.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009
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CROSSREFS
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Cf. A010468 Decimal expansion. - Harry J. Smith, Jun 02 2009
Sequence in context: A020813 A034188 A184849 * A110634 A324467 A151787
Adjacent sequences: A040004 A040005 A040006 * A040008 A040009 A040010
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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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