A040272 Continued fraction for sqrt(290).

17, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34

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) = 34 for n >= 1.

G.f.: 17*(1+x)/(1-x).

E.g.f.: 34*exp(x) - 17.

a(n) = 17*A040000(n). (End)

Example

17 + 1/(34 + 1/(34 + 1/(34 + 1/(34 + ...)))) = sqrt(290).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(290)), confrac);

Crossrefs

Cf. A040000, A041544/A041545 (convergents).

Sequence in context: A168579 A352981 A135637 * A062054 A164008 A013577

Adjacent sequences: A040269 A040270 A040271 * A040273 A040274 A040275

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved