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 A040032 #33 Jul 27 2025 04:20:25
%S A040032 6,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,
%T A040032 12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,4,12,
%U A040032 4,12,4,12,4,12,4,12,4,12,4
%N A040032 Continued fraction for sqrt(39).
%D A040032 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A040032 Harry J. Smith, <a href="/A040032/b040032.txt">Table of n, a(n) for n = 0..20000</a>
%H A040032 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040032 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040032 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A040032 From _Stefano Spezia_, Jul 27 2025: (Start)
%F A040032 a(n) = 2*A040008(n).
%F A040032 G.f.: 2*(3 + 2*x + 3*x^2)/(1 - x^2). (End)
%e A040032 6.2449979983983982058468931... = 6 + 1/(4 + 1/(12 + 1/(4 + 1/(12 + ...)))). - _Harry J. Smith_, Jun 05 2009
%p A040032 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040032 ContinuedFraction[Sqrt[39],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%t A040032 PadRight[{6},100,{12,4}] (* or *) Join[{6},LinearRecurrence[{0,1},{4,12},100]] (* _Harvey P. Dale_, Feb 09 2015 *)
%o A040032 (PARI) { allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(39)); for (n=0, 20000, write("b040032.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 05 2009
%Y A040032 Cf. A010493 (decimal expansion).
%K A040032 nonn,cofr,easy
%O A040032 0,1
%A A040032 _N. J. A. Sloane_