A081785 Continued cotangent for log(2).

0, 1, 5, 55, 14187, 314681540, 254841004490568887, 116515298784769863036311841843812470, 16752745298264669840183664790312981823804061660537952218518280274360024

Offset: 0

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

Crossrefs

Cf. A001620, A002666, A002667.

Programs

PARI

\p900
bn=vector(100);
bn[1]=log(2);
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

log(2) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).

Let b(0) = log(2), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).