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Continued cotangent for zeta(3).
0

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

%S 1,10,122,33429,1447509608,3251816299888840778,

%T 10657606087425320549792856871886476385,

%U 1233698091085791193532165615536619532897409600456434390187369062304735077655

%N Continued cotangent for zeta(3).

%F zeta(3)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=zeta(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]=zeta(3); ?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