A081788 Continued cotangent for sin(1).

0, 1, 11, 209, 778615, 3961986619787, 108027609649678328362291208, 12797763868538691769539594849146740548395979750179143, 2398705889323117848234063941075093304477004809996203196876904292203062137833411276780250923333345577605421

Offset: 0

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

References

• D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

Crossrefs

Cf. A002666, A002667, A002668.

Programs

PARI

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

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

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