A040420 Continued fraction for sqrt(442).

21, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42

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) = 42 for n >= 1.

G.f.: 21*(1+x)/(1-x).

E.g.f.: 42*exp(x) - 21.

a(n) = 21*A040000(n) = 7*A040006(n) = 3*A040042(n). (End)

Example

21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(442)), confrac);

Crossrefs

Cf. A041840/A041841 (convergents).

Cf. A040000, A040006, A040042.

Sequence in context: A362849 A120772 A260749 * A192130 A258188 A037978

Adjacent sequences: A040417 A040418 A040419 * A040421 A040422 A040423

Keyword

nonn,cofr,easy,less

Author

N. J. A. Sloane

Status

approved