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

1,1

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

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

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

Cf. A060213, A102168, A164290.

Sequence in context: A369250 A195270 A142111 * A243888 A033246 A141879

Adjacent sequences: A164286 A164287 A164288 * A164290 A164291 A164292

Keyword

nonn

Author

Carlos Alves, Aug 12 2009

Status

approved