A373408 Minimum of the n-th maximal antirun of squarefree numbers differing by more than one.

1, 2, 3, 6, 7, 11, 14, 15, 22, 23, 30, 31, 34, 35, 38, 39, 42, 43, 47, 58, 59, 62, 66, 67, 70, 71, 74, 78, 79, 83, 86, 87, 94, 95, 102, 103, 106, 107, 110, 111, 114, 115, 119, 123, 130, 131, 134, 138, 139, 142, 143, 146, 155, 158, 159, 166, 167, 174, 178, 179

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

The maximum is given by A007674.

An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.

Consists of 1 and all squarefree numbers n such that n - 1 is also squarefree.

Examples

			Row-minima of:
   1
   2
   3   5
   6
   7  10
  11  13
  14
  15  17  19  21
  22
  23  26  29
  30
  31  33
  34
  35  37
  38
  39  41
  42
  43  46
  47  51  53  55  57
		

Links

• Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers

Crossrefs

Functional neighbors: A005381, A006512, A007674, A072284, A373127, A373410, A373411.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A001223, A049093, A049094, A061398, A077641, A077643, A112925, A112926, A350842, A372683, A373123.

Programs

Mathematica

First/@Split[Select[Range[100],SquareFreeQ],#1+1!=#2&]//Most

Formula

a(1) = 1; a(n>1) = A007674(n-1) + 1.