A373415 Maximum of the n-th maximal run of squarefree numbers.

3, 7, 11, 15, 17, 19, 23, 26, 31, 35, 39, 43, 47, 51, 53, 55, 59, 62, 67, 71, 74, 79, 83, 87, 89, 91, 95, 97, 103, 107, 111, 115, 119, 123, 127, 131, 134, 139, 143, 146, 149, 151, 155, 159, 161, 163, 167, 170, 174, 179, 183, 187, 191, 195, 197, 199, 203, 206

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

The minimum is given by A072284.

A run of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by one.

Consists of all squarefree numbers k such that k + 1 is not squarefree.

Examples

			Row-maxima 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  58  59
		

Links

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

Crossrefs

Functional neighbors: A006093, A007674, A067774, A072284, A120992, A373413.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A049093, A049094, A061398, A069010, A077641, A077643, A112925, A112926, A143658, A372683, A373125, A373126.

Programs

Mathematica

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

Formula

a(n) = A070321(A072284(n+1) - 1).