A373573 - OEIS

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

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OFFSET

1,1

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?

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 antiruns of nonsquarefree numbers begin:

4 8

9 12 16 18 20 24

25 27

28 32 36 40 44

45 48

50 52 54 56 60 63

64 68 72 75

76 80

81 84 88 90 92 96 98

The a(n)-th rows are:

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

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]}]

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.

Sequence in context: A250646 A277068 A369904 * A092371 A187552 A157386

Adjacent sequences: A373570 A373571 A373572 * A373574 A373575 A373576

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 10 2024

STATUS

approved