%I #11 Sep 20 2012 02:38:35
%S 4,6,8,12,22,30,40,44,48,54,78,136,156,158,170,178,206,236,288,298,
%T 380,394,500,594,624,648,650,750,810,952,1062,1070,1162,1280,1500,
%U 1616,1680,1742,1764,2104,2120,2268,2332,2470,2494,2500,2600,2992,3094,3134
%N Even numbers m that have an odd number of Goldbach partitions whose lesser and greater elements each sum to a prime.
%H J. Stauduhar, <a href="/A216051/b216051.txt">Table of n, a(n) for n = 1..380</a>
%e 4, 6, 8, and 12 have just one Goldbach partition each, so the sum of the lesser and greater elements of each partition is prime, giving the first four terms in the sequence.
%e Three Goldbach partitions comprise 22: (3,19), (5,17) and (11,11). 3 + 5 + 11 = 19, and 11 + 17 + 19 = 47. Both 19 and 47 are prime, so a(5) = 22.
%t f[n_] := Module[{lst={}}, For[i=2, i<=n, i+=2, parts=Select[ IntegerPartitions[i, {2}], And@@PrimeQ /@#&]; If[And@@PrimeQ[Plus@@parts[[Range[1, Length[parts]], {1, 2}]]],
%t AppendTo[lst, i]];];lst]; f[1000](* J. Stuaduhar, Sep 18 2012 *)
%K nonn
%O 1,1
%A _J. Stauduhar_, Sep 16 2012
