A373200 Numbers k such that the k-th maximal antirun of squarefree numbers has length different from all prior maximal antiruns. Sorted positions of first appearances in A373127.

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

Offset

1,2

Comments

The unsorted version is A373128.

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
   15   17   19   21
   23   26   29
   47   51   53   55   57
  483  485  487  489  491  493

Mathematica

t=Length/@Split[Select[Range[10000], SquareFreeQ], #1+1!=#2&]//Most;
Select[Range[Length[t]], FreeQ[Take[t, #-1], t[[#]]]&]

Crossrefs

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

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

The unsorted version is A373128, firsts of A373127.

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

For composite runs we have A373400, unsorted A073051.

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

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

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

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

Sequence in context: A353078 A131725 A346370 * A332976 A032914 A088072

Adjacent sequences: A373197 A373198 A373199 * A373201 A373202 A373203

Keyword

nonn,more

Author

Gus Wiseman, Jun 10 2024

Status

approved