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A060977
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The nonprimes n!+2 ... n!+n are the a(n)-th string of n-1 prime-free consecutive terms, the first such one being the string of composite numbers A000230(k)+1 through A001632(k)-1 when n=2k, or through A001632(k)-2 when n=2k-1.
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0
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0, 1, 1, 6, 27, 208, 1755, 16363, 161685, 1736749, 20022517, 250566242, 3359504253
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OFFSET
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1,4
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COMMENTS
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The sequence grows rapidly, like the factorial function.
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LINKS
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EXAMPLE
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The prime-free sequence 4! + 2 through 4! + 4, i.e., {26, 27, 28}, ranks as the a(4) = 6th triple of consecutive composite numbers, as it comes after {8, 9, 10}, {14, 15, 16}, {20, 21, 22}, {24, 25, 26}, {25, 26, 27}.
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MATHEMATICA
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Do[ c = 0; a = Table[0, {n - 1} ]; k = 2; While[ k < n! + n + 1, a = Delete[a, 1]; a = Append[a, PrimeQ[k] ]; If[ Union[a] == {False}, c++ ]; k++ ]; Print[c], {n, 2, 12} ]
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CROSSREFS
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KEYWORD
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more,nonn,nice
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AUTHOR
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EXTENSIONS
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Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 25 2001
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STATUS
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approved
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