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A164289
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Sequence of twin primes p where the middle term p+1 has 5 prime factors (here p+2 is the associated twin prime, not listed).
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2
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71, 107, 179, 269, 311, 419, 659, 827, 881, 1019, 1031, 1049, 1091, 1427, 1451, 1607, 1931, 1949, 1997, 2027, 2141, 2309, 2549, 2711, 2729, 2789, 3329, 3467, 3539, 3767, 3821, 3851, 4019, 4091, 4229, 4259, 4481, 4649, 4931, 5417, 5651, 5741, 5867, 6089
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OFFSET
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1,1
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COMMENTS
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This sequence is similar to: A060213, with 3 prime factors in the middle number; A102168, with 4 prime factors in the middle number.
These sequences are of the form (p,p+1,p+2) with (p,p+2) twin primes and Omega(p+1)=m with m>=3 (m=1 or m=2 is impossible).
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LINKS
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Table of n, a(n) for n=1..44.
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EXAMPLE
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(71, 72, 73): Omega(72)=Omega(2*2*2*3*3)=5 and 71, 73 are twin primes.
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MATHEMATICA
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Omega = If[ # == 1, 0, Apply[Plus, Transpose[FactorInteger[ # ]][[2]]]] &; Wmil = Map[Omega, Range[1, 30000]]; Asequence = Flatten@Position[Partition[Wmil, 3, 1], {1, 5, 1}]
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CROSSREFS
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Cf. A060213, A102168, A164290
Sequence in context: A166576 A195270 A142111 * A033246 A141879 A026063
Adjacent sequences: A164286 A164287 A164288 * A164290 A164291 A164292
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KEYWORD
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nonn,changed
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Aug 12 2009
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STATUS
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approved
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