A081786 Continued cotangent for log(3).

1, 21, 1591, 5623795, 60586207387643, 11771746654268128293298294264, 223879928814222731378358322195036233470100990978181612407, 60370531495558553873551440308434816125184142701829318337696802178075590153432959525193229753905998692773283506988

Offset: 0

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

Crossrefs

Cf. A002666, A002667.

Programs

PARI

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

log(3) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).

Let b(0) = log(3), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).