Primes p such that p+2 and p+6 have 2 or fewer prime factors.
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 251, 257, 263, 281, 293, 307, 311, 317, 347, 353, 359, 389, 401, 409, 431, 443, 461, 467
1
See S000555 and S000556 for the case in which p+2 is prime.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
D.R. Heath-Brown and Xiannan Li, Almost prime tripes and Chen's Theorem, arXiv 1504.0533 (Apr 02 2015).
(Mma) f[n_] := Total[Transpose[FactorInteger[n]][[2]]]; Select[Prime[Range[500]], f[#+2] <= 2 && f[#+6] <= 2 &, 100]
Cf. S000555, S000556, S000558.
nonn
T. D. Noe, Apr 06 2015