A040870 - OEIS

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A040870

Continued fraction for sqrt(901).

4

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

(list; graph; refs; listen; history; text; internal format)

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