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A112888 Least semiprime of a cluster of just n semiprimes. 1
9, 33, 91, 299, 213, 1383, 3091, 8129 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
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}]
Join[{9}, Module[{osps=Select[Range[9, 10001, 2], PrimeOmega[#]==2&]}, #[[2]]& /@ Table[ SelectFirst[Partition[osps, n+2, 1], Union[ Differences[ Rest[ Most[#]]]]=={2}&&Last[#]-#[[-2]]!=2&&#[[2]]-#[[1]]!=2&], {n, 2, 8}]]] (* Harvey P. Dale, Jun 01 2016 *)
CROSSREFS
Sequence in context: A020326 A201024 A228170 * A048479 A031880 A231765
KEYWORD
nonn,fini,full
AUTHOR
Robert G. Wilson v, Nov 30 2005
EXTENSIONS
fini, full from Max Alekseyev, Feb 03 2010
STATUS
approved

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Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)