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Product of distinct primes p*q such that both 2p + q and p + 2q are prime numbers.
2

%I #8 May 21 2013 01:52:36

%S 15,21,35,39,51,65,95,119,141,155,159,161,185,201,219,221,291,305,329,

%T 341,365,371,395,471,485,501,515,519,579,581,611,669,681,695,779,791,

%U 815,831,851,905,921,959,989,1059,1079,1121,1139,1145,1149,1199,1205,1241

%N Product of distinct primes p*q such that both 2p + q and p + 2q are prime numbers.

%H Lei Zhou, <a href="/A225916/b225916.txt">Table of n, a(n) for n = 1..10000</a>

%e 15=3*5, both 2*3+5=11 and 3+2*5=13 are prime number, so 15 is a term of this sequence.

%t NextA046388[n_] := Block[{p1 = Prime[Range[2, PrimePi[Max[3, NextPrime[Ceiling@Sqrt[n + 1] - 1]]]]], p2}, p2 = Table[Max[NextPrime[p1[[i]]], NextPrime[Ceiling[(n + 1)/p1[[i]]] - 1]], {i, Length[p1]}]; Min[p1*p2]]; seed=1; Table[While[seed = NextA046388[seed]; fct = FactorInteger[seed]; p1 = fct[[1, 1]]; p2 = fct[[2, 1]]; c1 = 2*p1 + p2; c2 = p1 + 2*p2; ! ((PrimeQ[c1]) && (PrimeQ[c2]))]; seed, {i, 1, 52}]

%t nn = 1241; pq = Select[Range[nn], PrimeOmega[#] == 2 &]; p = Table[FactorInteger[r][[1, 1]], {r, pq}]; q = pq/p; t = {}; Do[If[PrimeQ[2 p[[i]] + q[[i]]] && PrimeQ[p[[i]] + 2 q[[i]]], AppendTo[t, pq[[i]]]], {i, Length[pq]}]; t (* _T. D. Noe_, May 21 2013 *)

%Y Cf. A046388.

%K nonn

%O 1,1

%A _Lei Zhou_, May 20 2013