A081784 Continued cotangent for zeta(3).

1, 10, 122, 33429, 1447509608, 3251816299888840778, 10657606087425320549792856871886476385, 1233698091085791193532165615536619532897409600456434390187369062304735077655

Offset: 0

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

Crossrefs

Cf. A001620, A002666, A002667.

Programs

PARI

\p900
bn=vector(100);
bn[1]=zeta(3);
b(n)=if(n<0,0,bn[n]);
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));

Formula

zeta(3) = cot(Sum_{n>=0} (-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)).