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Continued cotangent for zeta(2)=Pi^2/6.
0

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

%S 1,4,172,181307,241328833528,824652019956267685427678,

%T 768422457901766762303892554138930904416139509281,

%U 2110688056630901907060877896737932376507936264268382076456539236145849709148481095915090382331184

%N Continued cotangent for zeta(2)=Pi^2/6.

%F Pi^2/6=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Pi^2/6, 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]=Pi^2/6; ?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 0,2

%A _Benoit Cloitre_, Apr 10 2003