OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is 1/2 (Erdős, 1936). - Amiram Eldar, Sep 17 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős, On a problem of Chowla and some related problems, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; alternative link.
EXAMPLE
omega(1) = 0 < omega(2) = 1, hence 1 belongs to this sequence.
omega(4) = 1 = omega(5) = 1, hence 4 does not belong to this sequence.
omega(6) = 2 > omega(7) = 1, hence 6 does not belong to this sequence.
MATHEMATICA
Position[Partition[PrimeNu[Range[200]], 2, 1], _?(#[[1]]<#[[2]]&), 1, Heads-> False]//Flatten (* Harvey P. Dale, May 06 2018 *)
PROG
(PARI) for (n=1, 185, if (omega(n) < omega(n+1), print1 (n ", ")))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rémy Sigrist, Oct 26 2017
STATUS
approved