A377050 Position of first appearance of zero in the n-th differences of the nonsquarefree numbers, or 0 if it does not appear.

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

Links

Table of n, a(n) for n=0..28.

Lucas A. Brown, Python program.

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.

Cf. A000961, A007674, A053797, A053806, A061398, A072284, A084758, A112925, A120992, A376311, A376591, A377051.

Sequence in context: A145355 A351338 A110353 * A097720 A077806 A365731

Adjacent sequences: A377047 A377048 A377049 * A377051 A377052 A377053

Keyword

nonn,more

Author

Gus Wiseman, Oct 19 2024

Extensions

a(17)-a(28) from Lucas A. Brown, Oct 25 2024

Status

approved