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 A081780 #20 Apr 24 2025 17:47:38
%S A081780 1,3,16,405,672320,1352290629546,4817801789405093582066881,
%T A081780 125242334906904794515426191021121381708761081802849,
%U A081780 48098205042808280233282792304806428848378744166690329294696649253234314988369597043479633480454760546
%N A081780 Continued cotangent for square root of 3.
%F A081780 sqrt(3) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).
%F A081780 Let b(0) = sqrt(3), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).
%t A081780 Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, Sqrt[3], 8]] (* _Stefano Spezia_, Apr 24 2025 *)
%o A081780 (PARI) \p500
%o A081780 bn=vector(100); bn[1]=sqrt(3); b(n)=if(n<0,0,bn[n]);
%o A081780 for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))))
%o A081780 a(n)=floor(b(n+1))
%Y A081780 Cf. A002666, A002667.
%K A081780 nonn
%O A081780 0,2
%A A081780 _Benoit Cloitre_, Apr 10 2003