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 A040132 #23 Jul 08 2025 22:50:20 %S A040132 12,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24, %T A040132 24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24, %U A040132 24,24,24,24,24,24,24,24 %N A040132 Continued fraction for sqrt(145). %H A040132 <a href="/index/Con#confC">Index entries for continued fractions for constants</a> %H A040132 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A040132 From _Elmo R. Oliveira_, Feb 12 2024: (Start) %F A040132 a(n) = 24 for n >= 1. %F A040132 G.f.: 12*(1+x)/(1-x). %F A040132 E.g.f.: 24*exp(x) - 12. %F A040132 a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End) %e A040132 12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145). %p A040132 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'): %t A040132 ContinuedFraction[Sqrt[145],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 13 2011*) %Y A040132 Cf. A041264/A041265 (convergents), A176910 (decimal expansion). %Y A040132 Cf. A040000, A040002, A040006. %K A040132 nonn,cofr,easy %O A040132 0,1 %A A040132 _N. J. A. Sloane_