A040090 Continued fraction for sqrt(101).

10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• changed

Examples

			10 + 1/(20 + 1/(20 + 1/(20 + 1/(20 + ...)))) = sqrt(101).
		

Links

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

Crossrefs

Cf. A248803 (decimal expansion), A041180/A041181 (convergents).

Cf. A040000, A040002, A040020.

Programs

Maple

Digits := 200: convert(evalf(sqrt(101)),confrac,150,'cvgts'):

Mathematica

ContinuedFraction[Sqrt[101],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011*)
PadRight[{10},100,{20}] (* Harvey P. Dale, Apr 22 2022 *)

Formula

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

a(n) = 20 = A010859(n) for n >= 1.

G.f.: 10*(1+x)/(1-x).

E.g.f.: 20*exp(x) - 10.

a(n) = 10*A040000(n) = 5*A040002(n) = 2*A040020(n). (End)