A010128 Continued fraction for sqrt(29).

5, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10

Offset

0,1

References

Edward J. Barbeau, Pell's Equation, New York: Springer-Verlag, 2003, pp. 65-66, 68, Exercises 3.3 and 3.8.

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, pp. 96-97, 109.

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 (0,0,0,0,1).

Formula

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

Example

5.385164807134504031250710491... = 5 + 1/(2 + 1/(1 + 1/(1 + 1/(2 + ...)))). - Harry J. Smith, Jun 04 2009

Mathematica

ContinuedFraction[Sqrt[29], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{5}, 120, {10, 2, 1, 1, 2}] (* Harvey P. Dale, Apr 18 2017 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(29)); for (n=0, 20000, write("b010128.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Crossrefs

Cf. A010484 (Decimal expansion). - Harry J. Smith, Jun 04 2009

Sequence in context: A263007 A104714 A085119 * A348993 A180133 A197419

Adjacent sequences: A010125 A010126 A010127 * A010129 A010130 A010131

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved