A373573 Least k such that the k-th maximal antirun of nonsquarefree numbers has length n. Position of first appearance of n in A373409.

6, 1, 18, 8, 4, 2, 10, 52, 678

Offset: 1

Author

Gus Wiseman, Jun 10 2024

Keywords

• nonn

Comments

The sorted version is A373574.

An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.

Is this sequence finite? Are there only 9 terms?

Examples

			The maximal antiruns 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  68  72  75
  76  80
  81  84  88  90  92  96  98
  99
The a(n)-th rows are:
    49
     4    8
   148  150  152
    64   68   72   75
    28   32   36   40   44
     9   12   16   18   20   24
    81   84   88   90   92   96   98
   477  480  484  486  488  490  492  495
  6345 6348 6350 6352 6354 6356 6358 6360 6363
		

Links

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

Crossrefs

For composite runs we have A073051, firsts of A176246, sorted A373400.

For squarefree runs we have the triple (5,3,1), firsts of A120992.

For prime runs we have the triple (1,3,2), firsts of A175632.

For squarefree antiruns we have A373128, firsts of A373127, sorted A373200.

For nonsquarefree runs we have A373199 (assuming sorted), firsts of A053797.

For prime antiruns we have A373401, firsts of A027833, sorted A373402.

For composite antiruns we have the triple (2,7,1), firsts of A373403.

Positions of first appearances in A373409.

The sorted version is A373574.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A007674, A025157, A049094, A061399, A068781, A072284, A110969, A251092, A294242, A373410, A373412.

Programs

Mathematica

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