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

0,1

Links

Table of n, a(n) for n=0..55.

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (1).

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)

Example

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

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 *)

Crossrefs

Cf. A041364/A041365 (convergents).

Cf. A040000, A040002, A040042.

Sequence in context: A331099 A192354 A215970 * A335476 A296755 A297282

Adjacent sequences: A040179 A040180 A040181 * A040183 A040184 A040185

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved