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

0,1

Links

Table of n, a(n) for n=0..62.

Index entries for continued fractions for constants

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

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)

Example

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

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 *)

Crossrefs

Cf. A040000, A042740/A042741 (convergents).

Sequence in context: A004962 A271744 A121960 * A356176 A343340 A280011

Adjacent sequences: A040867 A040868 A040869 * A040871 A040872 A040873

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved