A010136 Continued fraction for sqrt(46).
6, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2
Offset: 0
Examples
6.782329983125268139064556326... = 6 + 1/(1 + 1/(3 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 06 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
- A. J. van der Poorten, An introduction to continued fractions, Unpublished.
- A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]
- G. Xiao, Contfrac
- Index entries for continued fractions for constants
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).
Crossrefs
Programs
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Mathematica
ContinuedFraction[Sqrt[46],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
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PARI
{ allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(46)); for (n=0, 20000, write("b010136.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009