A373199 - OEIS

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

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OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..9.

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

EXAMPLE

The maximal runs of nonsquarefree numbers begin:

8 9

24 25

27 28

44 45

48 49 50

63 64

The a(n)-th rows are:

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.

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]}]

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.

Sequence in context: A054566 A038144 A097977 * A136780 A301944 A128743

Adjacent sequences: A373196 A373197 A373198 * A373200 A373201 A373202

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 08 2024

STATUS

approved