|
|
A237288
|
|
Lexicographically earliest sequence of noncomposite numbers such that a(n)*n / sum(i=1..n, a(n) ) is strictly increasing.
|
|
1
|
|
|
1, 2, 3, 5, 7, 11, 17, 23, 31, 41, 53, 67, 83, 101, 127, 151, 179, 211, 251, 293, 337, 389, 443, 503, 569, 641, 719, 809, 907, 1009, 1117, 1229, 1361, 1493, 1637, 1787, 1949, 2129, 2309, 2503, 2707, 2917, 3137, 3371, 3613, 3877, 4153, 4441, 4751, 5059, 5381
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
If we replace in name of sequence:
noncomposite numbers -> nonprime numbers, then a(n) = A103517(n-1),
noncomposite numbers -> composite numbers, then a(n) = A103517(n),
noncomposite numbers -> primes, then a(n) = A237285(n),
noncomposite numbers -> natural numbers, then a(n) = A000027(n).
|
|
LINKS
|
|
|
EXAMPLE
|
For n=8: noncomposite number a(8) = 23 > a(7) = 17 is the smallest noncomposite number such that (8*23 / 69) > (7*17 / 46), a(8) is not 19 because (8*19 / (69-4)) < (7*17 / 46).
|
|
CROSSREFS
|
Cf. A008578 (noncomposite numbers).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|