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 A164289 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). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). LINKS EXAMPLE (71, 72, 73): Omega(72)=Omega(2*2*2*3*3)=5 and 71, 73 are twin primes. MATHEMATICA 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}] CROSSREFS Cf. A060213, A102168, A164290 Sequence in context: A166576 A195270 A142111 * A033246 A141879 A026063 Adjacent sequences:  A164286 A164287 A164288 * A164290 A164291 A164292 KEYWORD nonn,changed AUTHOR Carlos Alves (cjsalves(AT)gmail.com), Aug 12 2009 STATUS approved

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