A373128 - OEIS

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

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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

EXAMPLE

The maximal antiruns of squarefree numbers begin:

3 5

7 10

11 13

15 17 19 21

23 26 29

31 33

35 37

The a(n)-th rows are:

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.

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 08 2024

STATUS

approved