A079939 Greedy frac multiples of e: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=e.

1, 3, 7, 14, 39, 78, 394, 1001, 2002, 3003, 9545, 10546, 27634, 154257, 398959, 797918

Offset

1,2

Comments

The n-th greedy frac multiple of x is the smallest integer that does not cause sum(k=1..n,frac(a(k)*x)) to exceed unity; an infinite number of terms appear as the denominators of the convergents to the continued fraction of x.

Links

Table of n, a(n) for n=1..16.

Example

a(4) = 14 since frac(1x) + frac(3x) + frac(7x) + frac(14x) < 1, while frac(1x) + frac(3x) + frac(7x) + frac(k*x) > 1 for all k>7 and k<14.

Maple

Digits := 100: a := []: s := 0: x := exp(1.0): for n from 1 to 1000000 do: temp := evalf(s+frac(n*x)): if (temp<1.0) then a := [op(a), n]: print(n): s := s+evalf(frac(n*x)): fi: od: a;

Crossrefs

Cf. A007677 (denominators of convergents to e), A079934, A079937, A079940.

Sequence in context: A231397 A231464 A146920 * A147006 A146936 A184264

Adjacent sequences: A079936 A079937 A079938 * A079940 A079941 A079942

Keyword

more,nonn

Author

Benoit Cloitre and Paul D. Hanna, Jan 21 2003

Extensions

Two more terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 30 2003

Status

approved