A040110 Continued fraction for sqrt(122).

11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22

Offset

0,1

Links

Table of n, a(n) for n=0..53.

Index entries for continued fractions for constants

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

Formula

From Elmo R. Oliveira, Feb 11 2024: (Start)

a(n) = 22 for n >= 1.

G.f.: 11*(1+x)/(1-x).

E.g.f.: 22*exp(x) - 11.

a(n) = 11*A040000(n). (End)

Example

11 + 1/(22 + 1/(22 + 1/(22 + 1/(22 + ...)))) = sqrt(122).

Maple

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

Mathematica

ContinuedFraction[Sqrt[122], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2011*)

Crossrefs

Cf. A040000, A041220/A041221 (convergents).

Sequence in context: A138838 A139337 A231115 * A140452 A048136 A180054

Adjacent sequences: A040107 A040108 A040109 * A040111 A040112 A040113

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved