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 A164290 Sequence of twin prime p where the middle term p+1 has 6 prime factors (here p+2 is the associated twin prime, not listed). 3
 239, 599, 809, 1319, 1487, 2087, 2339, 2969, 3299, 4157, 4271, 4787, 5021, 5099, 5231, 5639, 5849, 6359, 6659, 7307, 7349, 9431, 9767, 10007, 10139, 10331, 10709, 10889, 11069, 11171, 11351, 11549, 11717, 11831, 11969, 12539, 13007, 13337 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is similar to A060213, A102168, A164289 respectively with 3, 4 and 5 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). Here m=6. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 EXAMPLE (239, 240, 241): Omega(240)=Omega(2*2*2*2*3*5)=6 and 239, 241 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, 6, 1}] Transpose[Select[Partition[Prime[Range[1600]], 2, 1], #[[2]]-#[[1]]==2 && PrimeOmega[ #[[1]]+1]==6&]][[1]] (* From Harvey P. Dale, May 15 2012 *) CROSSREFS Cf. A060213, A102168, A164289, A164291. Sequence in context: A152952 A142356 A142557 * A201787 A118574 A142854 Adjacent sequences:  A164287 A164288 A164289 * A164291 A164292 A164293 KEYWORD nonn AUTHOR Carlos Alves (cjsalves(AT)gmail.com), Aug 12 2009 STATUS approved

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