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 A040013 #34 Aug 25 2025 11:03:13
%S A040013 4,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,
%T A040013 8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,8,4,
%U A040013 8,4,8,4,8,4,8,4,8,4,8,4
%N A040013 Continued fraction for sqrt(18).
%C A040013 Decimal expansion of 74/165. - _R. J. Mathar_, Aug 25 2025
%D A040013 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040013 Harry J. Smith, <a href="/A040013/b040013.txt">Table of n, a(n) for n = 0..20000</a>
%H A040013 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040013 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040013 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A040013 G.f.: 4*(1 + x + x^2)/(1 - x^2). - _Stefano Spezia_, Jul 26 2025
%e A040013 4.242640687119285146405066172... = 4 + 1/(4 + 1/(8 + 1/(4 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 2009
%t A040013 ContinuedFraction[Sqrt[18],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A040013 PadRight[{4},120,{8,4}] (* _Harvey P. Dale_, Dec 31 2022 *)
%o A040013 (PARI) { allocatemem(932245000); default(realprecision, 31000); x=contfrac(sqrt(18)); for (n=0, 20000, write("b040013.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y A040013 Cf. A010474 Decimal expansion. - _Harry J. Smith_, Jun 03 2009
%K A040013 nonn,cofr,easy,changed
%O A040013 0,1
%A A040013 _N. J. A. Sloane_