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A377050
Position of first appearance of zero in the n-th differences of the nonsquarefree numbers, or 0 if it does not appear.
10
0, 0, 5, 11, 4, 129, 10, 89, 16, 161, 72, 77325, 71, 4870, 70, 253, 75, 737923, 166, 1648316, 165, 8753803, 164, 208366710, 163, 99489971, 162, 49493333, 161
OFFSET
0,3
COMMENTS
If a(29) is not 0, then it is > 10^12. - Lucas A. Brown, Oct 25 2024
EXAMPLE
The fourth differences of A013929 begin: -6, -2, 5, 0, -7, 9, -6, 6, -7, ... so a(4) = 4.
MATHEMATICA
nn=10000;
u=Table[Differences[Select[Range[nn], !SquareFreeQ[#]&], k], {k, 2, 16}];
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
m=Table[Position[u[[k]], 0][[1, 1]], {k, mnrm[Union[First/@Position[u, 0]]]}]
CROSSREFS
The version for primes is A376678, noncomposites A376855, composites A377037.
For squarefree instead of nonsquarefree numbers we have A377042.
For antidiagonal-sums we have A377047, absolute A377048.
For leading column we have A377049.
A000040 lists the primes, differences A001223, seconds A036263.
A005117 lists the squarefree numbers.
A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
A073576 counts integer partitions into squarefree numbers, factorizations A050320.
Sequence in context: A145355 A351338 A110353 * A097720 A077806 A365731
KEYWORD
nonn,more,new
AUTHOR
Gus Wiseman, Oct 19 2024
EXTENSIONS
a(17)-a(28) from Lucas A. Brown, Oct 25 2024
STATUS
approved