This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A040072 #33 Aug 25 2025 11:13:29
%S A040072 9,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
%T A040072 18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
%U A040072 18,18,18,18,18,18,18,18,18
%N A040072 Continued fraction for sqrt(82).
%H A040072 Harry J. Smith, <a href="/A040072/b040072.txt">Table of n, a(n) for n = 0..20000</a>
%H A040072 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040072 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040072 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040072 From _Elmo R. Oliveira_, Feb 10 2024: (Start)
%F A040072 a(n) = 18 = A010857(n) for n >= 1.
%F A040072 G.f.: 9*(1+x)/(1-x).
%F A040072 E.g.f.: 18*exp(x) - 9.
%F A040072 a(n) = 9*A040000(n) = 3*A040006(n). (End)
%e A040072 9.05538513813741662657380... = 9 + 1/(18 + 1/(18 + 1/(18 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 10 2009
%p A040072 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040072 ContinuedFraction[Sqrt[82],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 09 2011 *)
%t A040072 PadRight[{9},120,{18}] (* _Harvey P. Dale_, Oct 09 2020 *)
%o A040072 (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 A040072 Cf. A010533 (decimal expansion), A041144/A041145 (convergents), A248305 (Egyptian fraction).
%Y A040072 Cf. A040000, A040006.
%K A040072 nonn,cofr,easy,changed
%O A040072 0,1
%A A040072 _N. J. A. Sloane_