A040306 Continued fraction for sqrt(325).

18, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36

Offset

0,1

Links

Table of n, a(n) for n=0..62.

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

From Elmo R. Oliveira, Feb 14 2024: (Start)

a(n) = 36 for n >= 1.

G.f.: 18*(1+x)/(1-x).

E.g.f.: 36*exp(x) - 18.

a(n) = 18*A040000(n) = 9*A040002(n) = 6*A040006(n). (End)

Example

18 + 1/(36 + 1/(36 + 1/(36 + 1/(36 + ...)))) = sqrt(325).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(325)), confrac);

Mathematica

Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[325], 100]] (* or *) PadRight[{18}, 100, {36}] (* Harvey P. Dale, Dec 01 2020 *)

Crossrefs

Cf. A041612/A041613 (convergents).

Cf. A040000, A040002, A040006.

Sequence in context: A160844 A256878 A285318 * A346137 A303282 A073332

Adjacent sequences: A040303 A040304 A040305 * A040307 A040308 A040309

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved