%I #10 Mar 30 2012 18:39:16
%S 0,1,3,16,389,479403,590817544217,473341703003810973963339,
%T 269963674630454468003021997747122421847127276823,
%U 84255020180725066155718508782582560544360994462142096519461567461295107080386955008872752275165
%N Continued cotangent for the Gamma constant.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LehmerCotangentExpansion.html">Lehmer Cotangent Expansion</a>
%F Gamma=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Gamma, 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]=Euler; ?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. A001620, A002666, A002667.
%K nonn
%O 0,3
%A _Benoit Cloitre_, Apr 10 2003