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 A081785 #21 Apr 24 2025 01:31:21
%S A081785 0,1,5,55,14187,314681540,254841004490568887,
%T A081785 116515298784769863036311841843812470,
%U A081785 16752745298264669840183664790312981823804061660537952218518280274360024
%N A081785 Continued cotangent for log(2).
%F A081785 log(2) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).
%F A081785 Let b(0) = log(2), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).
%o A081785 (PARI) \p900
%o A081785 bn=vector(100);
%o A081785 bn[1]=log(2);
%o A081785 b(n)=if(n<0,0,bn[n]);
%o A081785 for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))));
%o A081785 a(n)=floor(b(n+1));
%Y A081785 Cf. A001620, A002666, A002667.
%K A081785 nonn
%O A081785 0,3
%A A081785 _Benoit Cloitre_, Apr 10 2003