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 A040380 #19 Feb 15 2024 13:01:59 %S A040380 20,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40, %T A040380 40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40, %U A040380 40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40 %N A040380 Continued fraction for sqrt(401). %H A040380 <a href="/index/Con#confC">Index entries for continued fractions for constants</a> %H A040380 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A040380 From _Elmo R. Oliveira_, Feb 15 2024: (Start) %F A040380 a(n) = 40 for n >= 1. %F A040380 G.f.: 20*(1+x)/(1-x). %F A040380 E.g.f.: 40*exp(x) - 20. %F A040380 a(n) = 20*A040000(n) = 10*A040002(n) = 5*A040012(n). (End) %e A040380 20 + 1/(40 + 1/(40 + 1/(40 + 1/(40 + ...)))) = sqrt(401). %p A040380 with(numtheory): Digits := 300: convert(evalf(sqrt(401)),confrac); %Y A040380 Cf. A041760/A041761 (convergents). %Y A040380 Cf. A040000, A040002, A040012. %K A040380 nonn,cofr,easy,less %O A040380 0,1 %A A040380 _N. J. A. Sloane_