OFFSET
1,1
COMMENTS
These are points at which the second differences (A376590) are nonzero.
LINKS
EXAMPLE
The squarefree numbers (A005117) are:
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, ...
with first differences (A076259):
1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, ...
with first differences (A376590):
0, 1, -1, 0, 2, -2, 1, -1, 0, 1, 0, 0, -1, 0, 2, 0, -2, 0, 1, -1, 0, 1, -1, 0, 1, ...
with nonzeros at (A376591):
2, 3, 5, 6, 7, 8, 10, 13, 15, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 31, 34, 36, ...
MATHEMATICA
Join@@Position[Sign[Differences[Select[Range[100], SquareFreeQ], 2]], 1|-1]
CROSSREFS
These are the nonzeros of A376590.
The complement is A376591.
For points of nonzero curvature: A333214 (prime), A376603 (composite), A376589 (non-perfect-power), A376595 (nonsquarefree), A376598 (prime-power), A376601 (non-prime-power).
For squarefree numbers: A076259 (first differences), A376590 (second differences), A376591 (inflection and undulation points).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 04 2024
STATUS
approved