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Continued cotangent for the Gamma constant.
0

%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