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

0,1

Comments

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

Decimal expansion of 323/990. - R. J. Mathar, Aug 22 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.: (3 + 2*x + 3*x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025

Example

3.464101615137754587054892683... = 3 + 1/(2 + 1/(6 + 1/(2 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009

Maple

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A010469 Decimal expansion, A010696.

Sequence in context: A061187 A248082 A021758 * A129354 A129628 A245691

Adjacent sequences: A040005 A040006 A040007 * A040009 A040010 A040011

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved