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

Author

Gus Wiseman, Jun 08 2024

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Links

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

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.

Programs

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]}]