A373199 Least k such that the k-th maximal run of nonsquarefree numbers has length n. Position of first appearance of n in A053797.

1, 2, 13, 68, 241, 6278, 61921, 311759, 2530539

Offset: 1

Author

Gus Wiseman, Jun 08 2024

Keywords

• nonn
• more

Comments

A run of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by one. The a(n)-th run of nonsquarefree numbers begins with A045882 = A051681, subset of A053806.

Examples

			The maximal runs of nonsquarefree numbers begin:
   4
   8   9
  12
  16
  18
  20
  24  25
  27  28
  32
  36
  40
  44  45
  48  49  50
  52
  54
  56
  60
  63  64
The a(n)-th rows are:
     4
     8     9
    48    49    50
   242   243   244   245
   844   845   846   847   848
For example, (48, 49, 50) is the first maximal run of 3 nonsquarefree numbers, so a(3) = 13.
		

Links

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

Crossrefs

For composite instead of nonsquarefree we have A073051.

The version for squarefree runs is A373128.

For prime instead of nonsquarefree we have A373400.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A007674, A020754, A045882, A120992, A061398, A061399, A068781, A101836, A251092, A294242, A373410, A373412.

Programs

Mathematica

seq=Length/@Split[Select[Range[10000],!SquareFreeQ[#]&],#1+1==#2&];
spna[y_]:=Max@@Select[Range[Length[y]],SubsetQ[y,Range[#]]&];
Table[Position[seq,i][[1,1]],{i,spna[seq]}]