A040013 Continued fraction for sqrt(18).

4, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4

Offset

0,1

Comments

Decimal expansion of 74/165. - R. J. Mathar, Aug 25 2025

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 (0,1).

Formula

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

Example

4.242640687119285146405066172... = 4 + 1/(4 + 1/(8 + 1/(4 + 1/(8 + ...)))). - Harry J. Smith, Jun 03 2009

Mathematica

ContinuedFraction[Sqrt[18], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 120, {8, 4}] (* Harvey P. Dale, Dec 31 2022 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 31000); x=contfrac(sqrt(18)); for (n=0, 20000, write("b040013.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

Crossrefs

Cf. A010474 Decimal expansion. - Harry J. Smith, Jun 03 2009

Sequence in context: A355234 A021227 A349778 * A153132 A167275 A273333

Adjacent sequences: A040010 A040011 A040012 * A040014 A040015 A040016

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved