OFFSET
1,2
COMMENTS
These are points at which the second differences (A376599) are nonzero.
Inclusive means 1 is a prime-power but not a non-prime-power. For the exclusive version, subtract 1 and shift left.
LINKS
EXAMPLE
The non-prime-powers inclusive (A024619) are:
6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, ...
with first differences (A375735):
4, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, ...
with first differences (A376599):
-2, 0, -1, 2, -1, -1, 0, 1, 0, 0, 0, 1, -2, 0, 0, 1, -1, 0, 1, 0, -1, 0, 1, 0, ...
with nonzero terms (A376601) at:
1, 3, 4, 5, 6, 8, 12, 13, 16, 17, 19, 21, 23, 25, 27, 28, 32, 34, 35, 36, 37, ...
MATHEMATICA
Join@@Position[Sign[Differences[Select[Range[100], !(#==1||PrimePowerQ[#])&], 2]], 1|-1]
CROSSREFS
These are the nonzeros of A376599.
The complement is A376600.
A007916 lists non-perfect-powers.
A057820 gives first differences of prime-powers inclusive.
For non-prime-powers: A375735/A375708 (first differences), A376599 (second differences), A376600 (inflections and undulations).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 05 2024
STATUS
approved