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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

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• A. J. van der Poorten, An introduction to continued fractions, Unpublished.
• A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]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

Cf. A010500 (decimal expansion), A041078/A041079 (convergents), A248272 (Egyptian fractions).

Cf. A190567.

Programs

Mathematica

ContinuedFraction[Sqrt[46],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

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