A226755 Numbers of the form p*q, p and q prime with q=2p-3.

9, 35, 77, 209, 299, 527, 989, 1829, 2627, 3239, 3569, 5459, 8777, 9869, 13529, 18527, 20099, 22577, 25199, 31877, 37127, 48827, 55277, 64979, 72389, 73919, 88409, 98789, 107879, 115439, 125249, 137549, 159329, 192509, 200027, 218129, 239777, 277139, 353219

Offset: 1

Author

José María Grau Ribas, Jun 16 2013

Keywords

• nonn

Comments

The smaller prime factor of a(n) = p = sopf(a(n))/3 + 1. The larger prime factor of a(n) = q = 2*sopf(a(n))/3 - 1. Furthermore, 2(sopf(a(n))/3 + 1) is representable as the sum of two primes in at least two ways since 2p = p + p = 3 + q. - Wesley Ivan Hurt, Jun 30 2013

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A129521, A156592, A226754.

Programs

Mathematica

fa = FactorInteger; t[n_]:=Length[fa[n]] == 2 && fa[n][[1,2]]== fa[n][[2, 2]] == 1 && 2 fa[n][[1, 1]]-3 == fa[n][[2, 1]]; Select[1+Range[200000], t]

PARI

list(lim)=my(v=List(), q); forprime(p=2, (sqrt(8*lim+9)+3)\4, if(isprime(q=2*p-3), listput(v, p*q))); Vec(v) \\ Charles R Greathouse IV, Nov 19 2013

Extensions

a(1) added by Charles R Greathouse IV, Nov 19 2013