A081789 Continued cotangent for cos(1).

0, 1, 3, 31, 1896, 4466398, 51545652359935, 7892797673015743066290382811, 79208317703482281896053478218775642522933780224074809198, 195824124605155340760338534459689354174423866004140103635128465652592661899008938733448659610261796713081609084855

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..9.

Formula

cos(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=cos(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]=cos(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: A194937 A141153 A144906 * A066976 A172645 A201604

Adjacent sequences: A081786 A081787 A081788 * A081790 A081791 A081792

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved