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 A040210 #23 Feb 14 2024 10:46:16 %S A040210 15,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30, %T A040210 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30, %U A040210 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30 %N A040210 Continued fraction for sqrt(226). %H A040210 <a href="/index/Con#confC">Index entries for continued fractions for constants</a> %H A040210 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A040210 From _Elmo R. Oliveira_, Feb 13 2024: (Start) %F A040210 a(n) = 30 for n >= 1. %F A040210 G.f.: 15*(1+x)/(1-x). %F A040210 E.g.f.: 30*exp(x) - 15. %F A040210 a(n) = 15*A040000(n) = 5*A040006(n) = 3*A040020(n). (End) %e A040210 15 + 1/(30 + 1/(30 + 1/(30 + 1/(30 + ...)))) = sqrt(226). %p A040210 with(numtheory): Digits := 300: convert(evalf(sqrt(226)),confrac); %Y A040210 Cf. A041420/A041421 (convergents). %Y A040210 Cf. A040000, A040006, A040020. %K A040210 nonn,cofr,easy %O A040210 0,1 %A A040210 _N. J. A. Sloane_