OFFSET
1,2
COMMENTS
The expression "local maximum" is understood here in a broad sense (as it were considering a flat-topped hill to be the same as a pointed hill): it is assumed that there is a local maximum a(n1) = a1 at n=n1 if there exists a neighborhood of n1 where the sequence is of the form {a0, a1, ..., a1, a2} with a0<a1 and a2<a1. Of course, in the case {a0,a1,a2}, where a1 is not repeated, this coincides with the usual definition of a local maximum in the strict sense.
This sequence is different from A020731, which concerns a global maximum.
Sometimes a local maximum is not the global maximum: for instance, with n = 59, the global maximum omega(binomial(59,22)) = 13 is obtained at k = 22, but there is a local maximum 12 at k = floor(59/2) = 29; this is the first occurrence absent from A020731, the next ones being 86, 91, 121, 123, 169, ... (see the link).
LINKS
Jean-François Alcover, Plot of omega(binomial(59,k))
MATHEMATICA
Select[Range[120], MatchQ[PrimeNu[Binomial[#, Range[Floor[#/2], #]]], {(x_) .., y_, ___} /; x > y] || # == 1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-François Alcover, Dec 10 2016
STATUS
approved