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

%I #20 Nov 20 2013 14:28:49

%S 9,35,77,209,299,527,989,1829,2627,3239,3569,5459,8777,9869,13529,

%T 18527,20099,22577,25199,31877,37127,48827,55277,64979,72389,73919,

%U 88409,98789,107879,115439,125249,137549,159329,192509,200027,218129,239777,277139,353219

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

%C 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

%H Charles R Greathouse IV, <a href="/A226755/b226755.txt">Table of n, a(n) for n = 1..10000</a>

%t 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]

%o (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

%Y Cf. A129521, A156592, A226754.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Jun 16 2013

%E a(1) added by _Charles R Greathouse IV_, Nov 19 2013