|
Search: id:A079939
|
|
|
| A079939 |
|
Greedy frac multiples of e: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=e. |
|
+0
8
|
|
| 1, 3, 7, 14, 39, 78, 394, 1001, 2002, 3003, 9545, 10546, 27634, 154257, 398959, 797918
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
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: A011947 A129629 A089526 this_sequence A106363 A128658 A001203
Adjacent sequences: A079936 A079937 A079938 this_sequence A079940 A079941 A079942
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2003
|
|
EXTENSIONS
|
Two more terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 30 2003
|
|
|
Search completed in 0.002 seconds
|
