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A112888
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Least semiprime of a cluster of just n semiprimes.
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0
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OFFSET
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1,1
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COMMENTS
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Clusters are sets composed of odd numbers.
If we include even numbers then the sequence would start 4,9,33 and terminates because in any group of four consecutive numbers greater than 4, 4 is a divisor to at least one member leaving a quotient greater than 1.
Any set of 9 consecutive odd numbers contain a multiple of 9, which not semiprime (unless it is equal to 9). Hence there are no 9 consecutive odd semiprimes.
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LINKS
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Table of n, a(n) for n=1..8.
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EXAMPLE
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a(8)=8129 because 8129=11*739, 8131=47*173, 8133=3*2711, 8135=5*1627, 8137=79*103, 8139=3*2713, 8141=7*1163, 8143=17*479.
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MATHEMATICA
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spQ[n_] := Plus @@ Last /@ FactorInteger@n == 2; f[n_] := Block[{k = 1}, While[ s[[k]] + 2n != s[[k + n]] || s[[k]] + 2n + 2 == s[[k + n + 1]], k++ ]; s[[k]]]; s = {}; Do[ If[ spQ[n], AppendTo[s, n]], {n, 9, 7*10^6, 2}]; Table[ f[n], {n, 0, 7}]
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CROSSREFS
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Cf. A001358, A097824, A082919.
Sequence in context: A005939 A020326 A201024 * A048479 A031880 A220165
Adjacent sequences: A112885 A112886 A112887 * A112889 A112890 A112891
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KEYWORD
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nonn,fini,full
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AUTHOR
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Robert G. Wilson v, Nov 30 2005
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EXTENSIONS
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fini, full from Max Alekseyev, Feb 03 2010
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STATUS
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approved
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