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A081788 Continued cotangent for sin(1).

%I A081788 #21 Apr 24 2025 01:30:45
%S A081788 0,1,11,209,778615,3961986619787,108027609649678328362291208,
%T A081788 12797763868538691769539594849146740548395979750179143,
%U A081788 2398705889323117848234063941075093304477004809996203196876904292203062137833411276780250923333345577605421
%N A081788 Continued cotangent for sin(1).
%D A081788 D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
%F A081788 sin(1) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).
%F A081788 Let b(0) = sin(1), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).
%o A081788 (PARI) \p900
%o A081788 bn=vector(100);
%o A081788 bn[1]=sin(1);
%o A081788 b(n)=if(n<0,0,bn[n]);
%o A081788 for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))));
%o A081788 a(n)=floor(b(n+1));
%Y A081788 Cf. A002666, A002667, A002668.
%K A081788 nonn
%O A081788 0,3
%A A081788 _Benoit Cloitre_, Apr 10 2003