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A264843
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Maximal numbers of consecutive positive integers congruent to 1 modulo 3 that are all squarefree.
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2
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1, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 1, 1, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 3, 3, 2, 3, 1, 1, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 3, 3
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OFFSET
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1,2
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COMMENTS
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a(n) takes only values 1,2,3, since from every four numbers == 1 (mod 3), at least one is divisible by 4, hence nonsquarefree.
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LINKS
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EXAMPLE
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From the first integers congruent to 1 (mod 3): 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, ..., the squarefree ones are (1), (7,10,13), (19,22), (31,34,37). So, a(1)=1, a(2)=3, a(3)=2, a(4)=3.
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MATHEMATICA
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Map[Count[#, True]&, DeleteCases[Split[Map[SquareFreeQ[3#-2]&, Range[500]]], {___, False, ___}]] (* Peter J. C. Moses, Nov 26 2015 *)
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PROG
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(PARI) lista(nn) = {nb = 0; for (n=0, nn, if (issquarefree(3*n+1), nb++, if (nb, print1(nb, ", ")); nb = 0); ); } \\ Michel Marcus, Dec 15 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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