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

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.

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).

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

Example

5.567764362830021922119471298... = 5 + 1/(1 + 1/(1 + 1/(3 + 1/(5 + ...)))). - Harry J. Smith, Jun 04 2009

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 *)

Prog

(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

Crossrefs

Cf. A010486 (decimal expansion).

Sequence in context: A180136 A346916 A359667 * A073050 A366426 A154740

Adjacent sequences: A010126 A010127 A010128 * A010130 A010131 A010132

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved