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A373574
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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.
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3
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OFFSET
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1,2
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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t=Length/@Split[Select[Range[100000], !SquareFreeQ[#]&], #1+1!=#2&];
Select[Range[Length[t]], FreeQ[Take[t, #-1], t[[#]]]&]
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CROSSREFS
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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 composite antiruns we have the triple (1,2,7), firsts of A373403.
Sorted positions of first appearances in A373409.
Cf. A007674, A025157, A049094, A061399, A068781, A072284, A077643, A110969, A251092, A294242, A373410, A373412.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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