OFFSET
1,1
COMMENTS
I call n a "k-apex" (or "apex of height k") of the arithmetical function f if n satisfies f(n-k) < ... < f(n-1) < f(n) > f(n+1) > .... > f(n+k).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
Omega(187) = 2 < Omega(188) = 3 < Omega(189) = 4 > Omega(190)= 3 > Omega(191) = 1, so 189 is a 2-apex of Omega.
MATHEMATICA
Select[Range[4, 10^4], Omega[ # - 2] < Omega[ # - 1] < Omega[ # ] > Omega[ # + 1] > Omega[ # + 2] &]
Flatten[Position[Partition[PrimeOmega[Range[4000]], 5, 1], _?(#[[1]]<#[[2]]<#[[3]]> #[[4]]> #[[5]]&), 1, Heads->False]]+2 (* Harvey P. Dale, Apr 11 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Nov 13 2002
STATUS
approved