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A373573
Least k such that the k-th maximal antirun of nonsquarefree numbers has length n. Position of first appearance of n in A373409.
9
6, 1, 18, 8, 4, 2, 10, 52, 678
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?
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
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
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.
Sequence in context: A250646 A277068 A369904 * A092371 A187552 A157386
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 10 2024
STATUS
approved