A040870 Continued fraction for sqrt(901).

30, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			30 + 1/(60 + 1/(60 + 1/(60 + 1/(60 + ...)))) = sqrt(901).
		

Links

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

Crossrefs

Cf. A040000, A042740/A042741 (convergents).

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(901)),confrac);

Mathematica

Block[{$MaxExtraPrecision=1000},ContinuedFraction[Sqrt[901],100]] (* or *) PadRight[{30},100,60] (* Harvey P. Dale, Sep 01 2014 *)

Formula

a(n) = 30*A040000(n). - Stefano Spezia, May 14 2023

From Elmo R. Oliveira, Feb 16 2024: (Start)

a(n) = 60 for n >= 1.

G.f.: 30*(1+x)/(1-x).

E.g.f.: 60*exp(x) - 30. (End)