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 A081781 #20 Apr 24 2025 17:33:58
%S A081781 2,23,2961,9798690,110528843365255,16850689692769666225948933906,
%T A081781 357017084742873887104901208145335336566095925224005385073,
%U A081781 137046393407742688281781643318644289249627231296779665713406441509975367310318242383523303176564909084594247359836
%N A081781 Continued cotangent for square root of 5.
%F A081781 sqrt(5) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).
%F A081781 Let b(0) = sqrt(5), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).
%t A081781 Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, Sqrt[5], 7]] (* _Stefano Spezia_, Apr 24 2025 *)
%o A081781 (PARI) bn=vector(100);
%o A081781 b(n)=if(n<0,0,bn[n]);
%o A081781 bn[1]=sqrt(5);
%o A081781 for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))));
%o A081781 a(n) = floor(b(n+1));
%Y A081781 Cf. A002666, A002667.
%K A081781 nonn
%O A081781 0,1
%A A081781 _Benoit Cloitre_, Apr 10 2003