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

%S 2,23,2961,9798690,110528843365255,16850689692769666225948933906,

%T 357017084742873887104901208145335336566095925224005385073,

%U 137046393407742688281781643318644289249627231296779665713406441509975367310318242383523303176564909084594247359836

%N Continued cotangent for square root of 5.

%F sqrt(5)=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(5); ?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 0,1

%A _Benoit Cloitre_, Apr 10 2003