A010134 Continued fraction for sqrt(43).

6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• cofr

Examples

			6.557438524302000652344109997... = 6 + 1/(1 + 1/(1 + 1/(3 + 1/(1 + ...)))) - _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
• Les Tablettes du Chercheur, Problem 364, pp. 11, Mai 15 1891
• G. Xiao, Contfrac
• Index entries for continued fractions for constants
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A010497 (decimal expansion).

Programs

Mathematica

ContinuedFraction[Sqrt[43],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

PARI

{ allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(43)); for (n=0, 20000, write("b010134.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

PARI

Vec((6*x^10+x^9+x^8+3*x^7+x^6+5*x^5+x^4+3*x^3+x^2+x+6)/(-x^10+1) + O(x^100)) \\ Colin Barker, Nov 01 2013

Formula

From Colin Barker, Nov 01 2013: (Start)

G.f.: (6*x^10+x^9+x^8+3*x^7+x^6+5*x^5+x^4+3*x^3+x^2+x+6)/(1-x^10).

a(n) = a(n-10) for n>10. (End)