A040552 Continued fraction for sqrt(577).

24, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48

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 15 2024: (Start)

a(n) = 48 for n >= 1.

G.f.: 24*(1+x)/(1-x).

E.g.f.: 48*exp(x) - 24.

a(n) = 24*A040000(n) = 12*A040002(n) = 8*A040006(n). (End)

Example

24 + 1/(48 + 1/(48 + 1/(48 + 1/(48 + ...)))) = sqrt(577).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(577)), confrac);

Crossrefs

Cf. A042104/A042105 (convergents).

Cf. A040000, A040002, A040006.

Sequence in context: A028992 A220515 A215148 * A199545 A098427 A335142

Adjacent sequences: A040549 A040550 A040551 * A040553 A040554 A040555

Keyword

nonn,cofr,easy,less

Author

N. J. A. Sloane

Status

approved