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 A040033 #30 Jul 27 2025 04:19:02
%S A040033 6,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,
%T A040033 12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,3,12,
%U A040033 3,12,3,12,3,12,3,12,3,12,3
%N A040033 Continued fraction for sqrt(40).
%D A040033 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040033 Harry J. Smith, <a href="/A040033/b040033.txt">Table of n, a(n) for n = 0..20000</a>
%H A040033 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040033 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040033 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A040033 From _Stefano Spezia_, Jul 27 2025: (Start)
%F A040033 a(n) = 3*A040005(n).
%F A040033 G.f.: 3*(2 + x + 2*x^2)/(1 - x^2). (End)
%e A040033 6.3245553203367586639977870... = 6 + 1/(3 + 1/(12 + 1/(3 + 1/(12 + ...)))). - _Harry J. Smith_, Jun 05 2009
%p A040033 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040033 ContinuedFraction[Sqrt[40],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%t A040033 LinearRecurrence[{0,1},{6,3,12},100] (* or *) PadRight[{6},100,{12,3}] (* _Harvey P. Dale_, Mar 03 2018 *)
%o A040033 (PARI) { allocatemem(932245000); default(realprecision, 32000); x=contfrac(sqrt(40)); for (n=0, 20000, write("b040033.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 05 2009
%Y A040033 Cf. A010494 (decimal expansion), A040005.
%K A040033 nonn,cofr,easy
%O A040033 0,1
%A A040033 _N. J. A. Sloane_