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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• changed

Examples

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

Links

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

Crossrefs

Cf. A040000, A041220/A041221 (convergents).

Programs

Maple

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

Mathematica

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

Formula

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

a(n) = 22 = A010861(n) for n >= 1.

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

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

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