%I #31 Feb 13 2024 08:16:22
%S 9,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
%T 18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
%U 18,18,18,18,18,18,18,18,18
%N Continued fraction for sqrt(82).
%H Harry J. Smith, <a href="/A040072/b040072.txt">Table of n, a(n) for n = 0..20000</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F From _Elmo R. Oliveira_, Feb 10 2024: (Start)
%F a(n) = 18 for n >= 1.
%F G.f.: 9*(1+x)/(1-x).
%F E.g.f.: 18*exp(x) - 9.
%F a(n) = 9*A040000(n) = 3*A040006(n). (End)
%e 9.05538513813741662657380... = 9 + 1/(18 + 1/(18 + 1/(18 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 10 2009
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[82],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 09 2011 *)
%t PadRight[{9},120,{18}] (* _Harvey P. Dale_, Oct 09 2020 *)
%o (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
%Y Cf. A010533 (decimal expansion), A041144/A041145 (convergents), A248305 (Egyptian fraction).
%Y Cf. A040000, A040006.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_