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A373574
Numbers k such that the k-th maximal antirun of nonsquarefree numbers has length different from all prior maximal antiruns. Sorted positions of first appearances in A373409.
3
1, 2, 4, 6, 8, 10, 18, 52, 678
OFFSET
1,2
COMMENTS
The unsorted version is A373573.
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:
4 8
9 12 16 18 20 24
28 32 36 40 44
49
64 68 72 75
81 84 88 90 92 96 98
148 150 152
477 480 484 486 488 490 492 495
6345 6348 6350 6352 6354 6356 6358 6360 6363
MATHEMATICA
t=Length/@Split[Select[Range[100000], !SquareFreeQ[#]&], #1+1!=#2&];
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.
For nonsquarefree runs we have A373199 (assuming sorted), firsts of A053797.
For squarefree antiruns: A373200, firsts of A373127, unsorted A373128.
For composite runs we have A373400, firsts of A176246, unsorted A073051.
For prime antiruns we have A373402, firsts of A027833, unsorted A373401.
For composite antiruns we have the triple (1,2,7), firsts of A373403.
Sorted positions of first appearances in A373409.
The unsorted version is A373573.
A005117 lists the squarefree numbers, first differences A076259.
A013929 lists the nonsquarefree numbers, first differences A078147.
Sequence in context: A111082 A100433 A254343 * A157006 A221991 A279254
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 10 2024
STATUS
approved