A040041 Continued fraction for sqrt(48).

6, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1

Offset

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 98.

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

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2^e) = 12, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 11/2^s). (End)

G.f.: (6 + x + 6*x^2)/(1 - x^2). - Stefano Spezia, Jul 27 2025

Example

6.9282032302755091741097853... = 6 + 1/(1 + 1/(12 + 1/(1 + 1/(12 + ...)))). - Harry J. Smith, Jun 06 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[48], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 24000); x=contfrac(sqrt(48)); for (n=0, 20000, write("b040041.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

Crossrefs

Cf. A010502 (decimal expansion).

Sequence in context: A342635 A107348 A342917 * A162933 A304252 A229085

Adjacent sequences: A040038 A040039 A040040 * A040042 A040043 A040044

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved