A373127 Length of the n-th maximal antirun of squarefree numbers differing by more than one.

1, 1, 2, 1, 2, 2, 1, 4, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 5, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 4, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 1, 2, 4, 2, 1, 4, 1, 3, 2, 1, 2, 1, 2, 1, 2, 2, 1, 4, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 4, 1, 3, 4, 1, 2, 1

Offset

1,3

Comments

The sum of this antirun is given by A373411.

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

Links

Table of n, a(n) for n=1..87.

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

Example

Row-lengths 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

Mathematica

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

Crossrefs

Positions of first appearances are A373128, sorted A373200.

Functional neighbors: A007674, A027833 (partial sums A029707), A120992, A373403, A373408, A373409, A373411.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

A077643 counts squarefree numbers with n bits, sum A373123.

Cf. A049093, A049094, A061398, A077641, A112925, A112926, A174965, A350842, A372683, A373125, A373126, A373197, A373198.

Sequence in context: A177954 A337312 A077053 * A363345 A344651 A308558

Adjacent sequences: A373124 A373125 A373126 * A373128 A373129 A373130

Keyword

nonn

Author

Gus Wiseman, Jun 05 2024

Status

approved