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 A040072 Continued fraction for sqrt(82). 7
 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 (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 (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

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Last modified May 25 03:08 EDT 2024. Contains 372782 sequences. (Running on oeis4.)