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

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

Offset

0,2

Links

Table of n, a(n) for n=0..7.

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)).

Prog

(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));

Crossrefs

Cf. A001620, A002666, A002667.

Sequence in context: A348085 A195631 A145245 * A222921 A318216 A006433

Adjacent sequences: A081780 A081781 A081782 * A081784 A081785 A081786

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved