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 A081787 #21 Apr 24 2025 01:30:58
%S A081787 1,4,208,51198,3265038057,25300257957809599598,
%T A081787 1548008157389016603196793951803038609594,
%U A081787 15445738611564165990406534887324277271178568836676520360367688416251534382546319
%N A081787 Continued cotangent for sqrt(e).
%D A081787 D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
%F A081787 sqrt(e) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).
%F A081787 Let b(0) = sqrt(e), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).
%o A081787 (PARI) \p900
%o A081787 bn=vector(100);
%o A081787 bn[1]=exp(1/2);
%o A081787 b(n)=if(n<0,0,bn[n]);
%o A081787 for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))));
%o A081787 a(n)=floor(b(n+1));
%Y A081787 Cf. A002666, A002667, A002668.
%K A081787 nonn
%O A081787 0,2
%A A081787 _Benoit Cloitre_, Apr 10 2003