%I #13 Jan 17 2015 19:20:51
%S 10,14,15,21,26,33,35,38,51,65,86,93,111,123,161,201,203,206,209,215,
%T 221,278,321,371,395,398,413,471,485,533,543,545,551,626,671,698,723,
%U 755,779,803,815,866,905,993,1046,1286,1349,1371,1383,1385,1403,1461
%N Numbers n that are a product of two primes j and k such that both n+j+k and n-j-k are primes.
%H Zak Seidov, <a href="/A088711/b088711.txt">Table of n, a(n) for n=1..1616, a(n)<200000</a>
%e a(1)=10 because 10 has only one pair of prime factors (2 and 5) and both 10+2+5 and 10-2-5 (17 and 3) are primes.
%t a[n_]:={1,1}==Last/@FactorInteger[n];b[n_]:=First[First/@FactorInteger[n]]+Last[First/@FactorInteger[n]];Select[Range[6,3000],a[#]&&PrimeQ[#-b[#]]&&PrimeQ[#+b[#]]&] (* _Vladimir Joseph Stephan Orlovsky_, Mar 03 2011 *)
%t Reap[Do[fi=FactorInteger[n]; la=Last/@fi; If[{1,1}==la, pq=fi[[1,1]]+fi[[2,1]];If[PrimeQ[n-pq] && PrimeQ[n+pq], Sow[n]]], {n,6,200000}]][[2,1]] (* used to create b-file, _Zak Seidov_, Mar 04 2011 *)
%Y Cf. A001358, A088709, A088710.
%K nonn
%O 1,1
%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 11 2003