A165986 Even semiprimes n such that (the largest prime factor of n) + 4 is prime.

6, 14, 26, 38, 74, 86, 134, 158, 194, 206, 218, 254, 326, 386, 446, 458, 554, 614, 626, 698, 758, 794, 878, 914, 926, 974, 998, 1226, 1286, 1346, 1478, 1514, 1538, 1646, 1706, 1718, 1754, 1766, 1814, 1874, 1934, 2018, 2174, 2186, 2426, 2558, 2594, 2606

Offset: 1

Author

Giovanni Teofilatto, Oct 03 2009, Jun 26 2011

Keywords

• nonn
• easy

Comments

Also numbers n of the form 2p such that p and p+4 are prime.

n is congruent to 2 modulo 3 for n > 6.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Magma

[ 2*p: p in PrimesUpTo(1500) | IsPrime(p+4) ]; // Klaus Brockhaus, Jun 26 2011

Mathematica

Select[Range[2,3000,2],PrimeOmega[#]==2&&PrimeQ[FactorInteger[#][[-1,1]]+4]&] (* Harvey P. Dale, Mar 09 2021 *)

PARI

forprime(p=2,1e3,if(isprime(p+4),print1(p+p", "))) \\ Charles R Greathouse IV, Jun 26 2011

Formula

a(n) = 2*A023200(n). - R. J. Mathar, Jun 23 2011

Extensions

Definition clarified by Harvey P. Dale, Jul 14 2021