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

0,1

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

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

a(n) = 20 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)

Example

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

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 *)

Crossrefs

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

Cf. A040000, A040002, A040020.

Sequence in context: A069555 A069035 A245065 * A183195 A098176 A362669

Adjacent sequences: A040087 A040088 A040089 * A040091 A040092 A040093

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved