A081788 Continued cotangent for sin(1).

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

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..8.

Formula

sin(1)=cot(sum(n>=0, n, (-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)).

Prog

(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=sin(1); ?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. A002666, A002667, A002668.

Sequence in context: A374095 A131216 A034909 * A358321 A060496 A280072

Adjacent sequences: A081785 A081786 A081787 * A081789 A081790 A081791

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved