A040032 Continued fraction for sqrt(39).

6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4

Offset

0,1

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

From Stefano Spezia, Jul 27 2025: (Start)

a(n) = 2*A040008(n).

G.f.: 2*(3 + 2*x + 3*x^2)/(1 - x^2). (End)

Example

6.2449979983983982058468931... = 6 + 1/(4 + 1/(12 + 1/(4 + 1/(12 + ...)))). - Harry J. Smith, Jun 05 2009

Maple

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

Mathematica

ContinuedFraction[Sqrt[39], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{6}, 100, {12, 4}] (* or *) Join[{6}, LinearRecurrence[{0, 1}, {4, 12}, 100]] (* Harvey P. Dale, Feb 09 2015 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(39)); for (n=0, 20000, write("b040032.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

Crossrefs

Cf. A010493 (decimal expansion).

Sequence in context: A357128 A141270 A393468 * A239394 A376614 A006582

Adjacent sequences: A040029 A040030 A040031 * A040033 A040034 A040035

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved