A237288 Lexicographically earliest sequence of noncomposite numbers such that a(n)*n / sum(i=1..n, a(n) ) is strictly increasing.

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

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

Table of n, a(n) for n=1..51.

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).

Sequence in context: A267944 A113161 A038953 * A293074 A005105 A086566

Adjacent sequences: A237285 A237286 A237287 * A237289 A237290 A237291

Keyword

nonn

Author

Jaroslav Krizek, Feb 28 2014

Status

approved