A373128 Least k such that the k-th maximal antirun of squarefree numbers has length n. Position of first appearance of n in A373127.

1, 3, 10, 8, 19, 162, 1853, 2052, 1633, 26661, 46782, 3138650, 1080330

Offset

1,2

Comments

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..13.

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

Example

The maximal antiruns of squarefree numbers begin:
   1
   2
   3   5
   6
   7  10
  11  13
  14
  15  17  19  21
  22
  23  26  29
  30
  31  33
  34
  35  37
The a(n)-th rows are:
    1
    3    5
   23   26   29
   15   17   19   21
   47   51   53   55   57
  483  485  487  489  491  493
For example, (23, 26, 29) is the first maximal antirun of 3 squarefree numbers, so a(3) = 10.

Mathematica

t=Length/@Split[Select[Range[10000], SquareFreeQ[#]&], #1+1!=#2&]//Most;
spnm[y_]:=Max@@NestWhile[Most, y, Union[#]!=Range[Max@@#]&];
Table[Position[t, k][[1, 1]], {k, spnm[t]}]

Crossrefs

For composite instead of squarefree we have A073051.

Positions of first appearances in A373127.

The version for nonsquarefree runs is A373199, firsts of A053797.

For prime instead of squarefree we have A373401, firsts of A027833.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A006512, A007674, A049093, A068781, A072284, A077641, A120992, A174965, A251092, A373198, A373408, A373411.

Sequence in context: A033152 A281178 A280461 * A222345 A353618 A202339

Adjacent sequences: A373125 A373126 A373127 * A373129 A373130 A373131

Keyword

nonn,more

Author

Gus Wiseman, Jun 08 2024

Status

approved