A225916 Product of distinct primes p*q such that both 2p + q and p + 2q are prime numbers.

15, 21, 35, 39, 51, 65, 95, 119, 141, 155, 159, 161, 185, 201, 219, 221, 291, 305, 329, 341, 365, 371, 395, 471, 485, 501, 515, 519, 579, 581, 611, 669, 681, 695, 779, 791, 815, 831, 851, 905, 921, 959, 989, 1059, 1079, 1121, 1139, 1145, 1149, 1199, 1205, 1241

Offset

1,1

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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}]
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 *)

Crossrefs

Cf. A046388.

Sequence in context: A346812 A296244 A309005 * A128279 A099611 A081934

Adjacent sequences: A225913 A225914 A225915 * A225917 A225918 A225919

Keyword

nonn

Author

Lei Zhou, May 20 2013

Status

approved