A040182 Continued fraction for sqrt(197).

14, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			14 + 1/(28 + 1/(28 + 1/(28 + 1/(28 + ...)))) = sqrt(197).
		

Links

• Index entries for continued fractions for constants
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A041364/A041365 (convergents).

Cf. A040000, A040002, A040042.

Programs

Maple

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

Mathematica

ContinuedFraction[Sqrt[197],300] (* Vladimir Joseph Stephan Orlovsky, Mar 28 2011 *)
PadRight[{14},120,{28}] (* Harvey P. Dale, May 02 2022 *)

Formula

From Elmo R. Oliveira, Feb 13 2024: (Start)

a(n) = 28 for n >= 1.

G.f.: 14*(1+x)/(1-x).

E.g.f.: 28*exp(x) - 14.

a(n) = 14*A040000(n) = 7*A040002(n) = 2*A040042(n). (End)