A010129 Continued fraction for sqrt(31).

5, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			5.567764362830021922119471298... = 5 + 1/(1 + 1/(1 + 1/(3 + 1/(5 + ...)))). - _Harry J. Smith_, Jun 04 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 (0,0,0,0,0,0,0,1).

Crossrefs

Cf. A010486 (decimal expansion).

Programs

Mathematica

ContinuedFraction[Sqrt[31],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{5},120,{10,1,1,3,5,3,1,1}] (* Harvey P. Dale, Jan 10 2025 *)

PARI

{ allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(31)); for (n=0, 20000, write("b010129.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Formula

G.f.: (5 + x + x^2 + 3*x^3 + 5*x^4 + 3*x^5 + x^6 + x^7 + 5*x^8)/(1 - x^8). - Stefano Spezia, Jul 26 2025