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).

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

Offset: 1

Author

Carlos Alves, Aug 12 2009

Keywords

• nonn

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.

Examples

			(239, 240, 241): Omega(240)=Omega(2*2*2*2*3*5)=6 and 239, 241 are twin primes.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A060213, A102168, A164289, A164291.

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, 6, 1}]
Transpose[Select[Partition[Prime[Range[1600]],2,1],#[[2]]-#[[1]]==2 && PrimeOmega[ #[[1]]+1]==6&]][[1]] (* Harvey P. Dale, May 15 2012 *)