A081787 Continued cotangent for sqrt(e).

1, 4, 208, 51198, 3265038057, 25300257957809599598, 1548008157389016603196793951803038609594, 15445738611564165990406534887324277271178568836676520360367688416251534382546319

Offset

0,2

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..7.

Formula

sqrt(e)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sqrt(e), 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]=sqrt(e); ?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: A222282 A087924 A201978 * A293159 A340176 A038790

Adjacent sequences: A081784 A081785 A081786 * A081788 A081789 A081790

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved