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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• changed

Comments

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

Examples

			4.242640687119285146405066172... = 4 + 1/(4 + 1/(8 + 1/(4 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 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 (0,1).

Crossrefs

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

Programs

Mathematica

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

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

Formula

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