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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).
3
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
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 is a term since 71 and 73 are twin primes and Omega(71 + 1) = Omega(72) = Omega(2*2*2*3*3) = 5.
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}]
Select[Partition[Prime[Range[800]], 2, 1], #[[2]]-#[[1]]==2&&PrimeOmega[ #[[1]]+1] ==5&][[All, 1]] (* Harvey P. Dale, Apr 02 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Carlos Alves, Aug 12 2009
STATUS
approved