A040702 Continued fraction for sqrt(730).

27, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54

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) = 54 for n >= 1.

G.f.: 27*(1+x)/(1-x).

E.g.f.: 54*exp(x) - 27.

a(n) = 27*A040000(n) = 9*A040006(n) = 3*A040072(n). (End)

Example

27 + 1/(54 + 1/(54 + 1/(54 + 1/(54 + ...)))) = sqrt(730).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(730)), confrac);

Crossrefs

Cf. A042404/A042405 (convergents).

Cf. A040000, A040006, A040072.

Sequence in context: A255364 A082915 A183032 * A305548 A306824 A043323

Adjacent sequences: A040699 A040700 A040701 * A040703 A040704 A040705

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved