A040072 Continued fraction for sqrt(82).

9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Index entries for continued fractions for constants

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

Formula

From Elmo R. Oliveira, Feb 10 2024: (Start)

a(n) = 18 for n >= 1.

G.f.: 9*(1+x)/(1-x).

E.g.f.: 18*exp(x) - 9.

a(n) = 9*A040000(n) = 3*A040006(n). (End)

Example

9.05538513813741662657380... = 9 + 1/(18 + 1/(18 + 1/(18 + 1/(18 + ...)))). - Harry J. Smith, Jun 10 2009

Maple

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

Mathematica

ContinuedFraction[Sqrt[82], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
PadRight[{9}, 120, {18}] (* Harvey P. Dale, Oct 09 2020 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 51000); x=contfrac(sqrt(82)); for (n=0, 20000, write("b040072.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 10 2009

Crossrefs

Cf. A010533 (decimal expansion), A041144/A041145 (convergents), A248305 (Egyptian fraction).

Cf. A040000, A040006.

Sequence in context: A103700 A158623 A046125 * A034728 A129855 A250769

Adjacent sequences: A040069 A040070 A040071 * A040073 A040074 A040075

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved