OFFSET
1,2
COMMENTS
Warning: Do not confuse with A246655 (prime-powers exclusive).
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, ...
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, ...
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, ...
with sorted first appearances at (A376655):
1, 2, 3, 5, 6, 30, 61, 150, 514, 1025, 5153, 13390, 13391, ...
MATHEMATICA
q=Differences[Select[Range[1000], SquareFreeQ], 2];
Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&]
CROSSREFS
These are the sorted positions of first appearances in A376590.
For primes instead of squarefree numbers we have A376656.
For second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376593 (nonsquarefree), A376596 (prime-power inclusive), A376599 (non-prime-power inclusive).
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Oct 07 2024
EXTENSIONS
a(14)-a(19) from Chai Wah Wu, Oct 07 2024
STATUS
approved