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%I #11 Jul 11 2015 00:45:10
%S 0,1,11,209,778615,3961986619787,108027609649678328362291208,
%T 12797763868538691769539594849146740548395979750179143,
%U 2398705889323117848234063941075093304477004809996203196876904292203062137833411276780250923333345577605421
%N Continued cotangent for sin(1).
%D D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
%F sin(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); 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 (PARI) ?bn=vector(100); b(n)=if(n<0,0,bn[n]); bn[1]=sin(1); ?for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)))) ?a(n)=floor(b(n+1))
%Y Cf. A002666, A002667, A002668.
%K nonn
%O 0,3
%A _Benoit Cloitre_, Apr 10 2003