A040008 Continued fraction for sqrt(12).

3, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• changed

Comments

Eventual period is (2,6). - Zak Seidov, Mar 05 2011

Decimal expansion of 323/990. - R. J. Mathar, Aug 22 2025

Examples

			3.464101615137754587054892683... = 3 + 1/(2 + 1/(6 + 1/(2 + 1/(6 + ...)))). - _Harry J. Smith_, Jun 02 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. A010469 Decimal expansion, A010696.

Programs

Maple

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

Mathematica

ContinuedFraction[Sqrt[12],300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

PARI

{ allocatemem(932245000); default(realprecision, 24000); x=contfrac(sqrt(12)); for (n=0, 20000, write("b040008.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009

Formula

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