A040600 Continued fraction for sqrt(626).

25, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50

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) = 50 for >= 1.

G.f.: 25*(1+x)/(1-x).

E.g.f.: 50*exp(x) - 25.

a(n) = 25*A040000(n) = 5*A040020(n). (End)

Example

25 + 1/(50 + 1/(50 + 1/(50 + 1/(50 + ...)))) = sqrt(626).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(626)), confrac);

Crossrefs

Cf. A042200/A042201 (convergents).

Cf. A040000, A040020.

Sequence in context: A049228 A309828 A076637 * A277190 A236849 A236834

Adjacent sequences: A040597 A040598 A040599 * A040601 A040602 A040603

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved