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A040073 Continued fraction for sqrt(83). 3
9, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9 (list; graph; refs; listen; history; text; internal format)
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 (0, 1).

FORMULA

a(n) = (1/2)(27 + 9*(-1)^n) - 9*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 10 2009

EXAMPLE

9.1104335791442988819456261... = 9 + 1/(9 + 1/(18 + 1/(9 + 1/(18 + ...)))). - Harry J. Smith, Jun 10 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[83], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)

LinearRecurrence[{0, 1}, {9, 9, 18}, 70] (* or *) PadRight[{9}, 70, {18, 9}] (* Harvey P. Dale, Jan 25 2018 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 45000); x=contfrac(sqrt(83)); for (n=0, 20000, write("b040073.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 10 2009

CROSSREFS

Cf. A010534 Decimal expansion. - Harry J. Smith, Jun 10 2009

Sequence in context: A003885 A168390 A321659 * A003886 A065999 A168419

Adjacent sequences:  A040070 A040071 A040072 * A040074 A040075 A040076

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 23 03:25 EDT 2019. Contains 325230 sequences. (Running on oeis4.)