A010133 Continued fraction for sqrt(41).
6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12
Offset: 0
Examples
6.40312423743284868648821767... = 6 + 1/(2 + 1/(2 + 1/(12 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 05 2009
References
- James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
Links
- 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 (0,0,1).
Crossrefs
Programs
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Mathematica
ContinuedFraction[Sqrt[41],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
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PARI
{ allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(41)); for (n=0, 20000, write("b010133.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009
Formula
From Elmo R. Oliveira, Aug 03 2024: (Start)
G.f.: 2*(3 + x + x^2 + 3*x^3)/((1 - x)*(1 + x + x^2)).
a(n) = a(n-3), n > 3. (End)