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A165936
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A sequence of triples of squarefree consecutive integers each composed of exactly three primes.
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0
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1309, 1310, 1311, 1885, 1886, 1887, 2013, 2014, 2015, 2665, 2666, 2667, 3729, 3730, 3731, 5133, 5134, 5135, 6061, 6062, 6063, 6213, 6214, 6215, 6305, 6306, 6307, 6477, 6478, 6479, 6853, 6854, 6855, 6985, 6986, 6987, 7257, 7258, 7259, 7953, 7954, 7955, 8393
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OFFSET
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1,1
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LINKS
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FORMULA
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a(3n+1) = A066509(n+1); a(3n+2) = 1 + a(3n+1); a(3n+3) = 1 + a(3n+2). - R. J. Mathar, Nov 27 2011
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EXAMPLE
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1309 = 7 * 11 * 17, 1310 = 2 * 5 * 131, 1311 = 3 * 19 * 23.
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MATHEMATICA
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Select[Partition[Range[10000], 3, 1], AllTrue[#, SquareFreeQ]&&Union[ PrimeOmega[ #]] == {3}&]//Flatten (* Harvey P. Dale, Oct 02 2017 *)
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PROG
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(Magma) a:=[]; f:=func<n|forall{n+s: s in [0, 1, 2] |IsSquarefree(n+s) and #PrimeDivisors(n+s) eq 3}>; for k in [2..8500] do if f(k) then a:=a cat [k, k+1, k+2]; end if; end for; a; // Marius A. Burtea, Oct 05 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Richard L. Peterson (rl_pete(AT)yahoo.com), Oct 01 2009
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EXTENSIONS
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STATUS
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approved
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