%I #11 Jul 29 2015 09:39:43

%S 0,1,5,55,14187,314681540,254841004490568887,

%T 116515298784769863036311841843812470,

%U 16752745298264669840183664790312981823804061660537952218518280274360024

%N Continued cotangent for log(2).

%F log(2)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=log(2), 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) b(n)=if(n<0,0,bn[n]);

%o bn=vector(100);bn[1]=log(2); for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))))

%o a(n)=floor(b(n+1))

%Y Cf. A001620, A002666, A002667.

%K nonn

%O 0,3

%A _Benoit Cloitre_, Apr 10 2003