A375711 Numbers k such that A013929(k+1) - A013929(k) = 3. In other words, the k-th nonsquarefree number is 3 less than the next nonsquarefree number.

3, 16, 23, 27, 31, 44, 46, 51, 55, 60, 68, 74, 79, 86, 95, 101, 105, 107, 112, 116, 121, 126, 129, 146, 147, 152, 159, 164, 167, 172, 177, 182, 185, 191, 195, 199, 204, 209, 220, 223, 229, 234, 237, 242, 244, 257, 262, 270, 275, 285, 286, 291, 299, 305, 312

Offset

1,1

Comments

The difference of consecutive nonsquarefree numbers is at least 1 and at most 4, so there are four disjoint sequences of this type:

- A375709 (difference 1)

- A375710 (difference 2)

- A375711 (difference 3)

- A375712 (difference 4)

Links

Table of n, a(n) for n=1..55.

Formula

Complement of A375709 U A375710 U A375712.

Example

The initial nonsquarefree numbers are 4, 8, 9, 12, 16, 18, 20, 24, 25, which first increase by 3 after the third term.

Mathematica

Join@@Position[Differences[Select[Range[1000], !SquareFreeQ[#]&]], 3]

Crossrefs

Positions of 3's in A078147.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.

A375707 counts squarefree numbers between consecutive nonsquarefree numbers.

Cf. A007674, A014689, A049094, A061399, A068781, A072284, A110969, A120992, A294242, A373409, A375927.

Sequence in context: A218625 A028687 A201274 * A101132 A153723 A091273

Adjacent sequences: A375708 A375709 A375710 * A375712 A375713 A375714

Keyword

nonn

Author

Gus Wiseman, Sep 09 2024

Status

approved