%I #9 Mar 30 2012 18:39:16

%S 1,3,16,405,672320,1352290629546,4817801789405093582066881,

%T 125242334906904794515426191021121381708761081802849,

%U 48098205042808280233282792304806428848378744166690329294696649253234314988369597043479633480454760546

%N Continued cotangent for square root of 3.

%F sqrt(3)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); 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))

%o (PARI) ?bn=vector(100); b(n)=if(n<0,0,bn[n]); bn[1]=sqrt(3); ?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.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Apr 10 2003