A081783 Continued cotangent for zeta(2) = Pi^2/6.

1, 4, 172, 181307, 241328833528, 824652019956267685427678, 768422457901766762303892554138930904416139509281, 2110688056630901907060877896737932376507936264268382076456539236145849709148481095915090382331184

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Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

Crossrefs

Cf. A001620, A002666, A002667.

Programs

PARI

\p900
bn=vector(100);
bn[1]=Pi^2/6;
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

Pi^2/6 = cot(Sum_{n>=0} (-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)).