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).

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

Author

Carlos Alves, Aug 12 2009

Keywords

• nonn

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).

Examples

			71 is a term since 71 and 73 are twin primes and Omega(71 + 1) = Omega(72) = Omega(2*2*2*3*3) = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060213, A102168, A164290.

Programs

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 *)