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%I #6 Jun 15 2020 22:33:35
%S 12,18,20,24,26,32,36,38,44,48,50,56,62,66,68,74,78,80,86,92,104,108,
%T 110,114,116,122,128,134,140,144,146,152,156,158,164,170,176,182,186,
%U 188,194,198,200,204,206,212,218,224,230,234,236,242,246,248,254,260,266
%N Even numbers with a Goldbach partition (p,q), p < q, such that p and q can be written as the sum of two primes.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%e 12 is in the sequence since 12 = 7 + 5 (distinct primes), 7 = 5 + 2 (both prime) and 5 = 3 + 2 (both prime).
%e 18 is in the sequence since 18 = 13 + 5 (distinct primes), 13 = 11 + 2 (both prime) and 5 = 3 + 2 (both prime).
%t Table[If[Sum[(PrimePi[i - 2] - PrimePi[i - 3]) (PrimePi[2 n - i - 2] - PrimePi[2 n - i - 3]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n - 1}] > 0, 2 n, {}], {n, 150}] // Flatten
%K nonn,easy
%O 1,1
%A _Wesley Ivan Hurt_, Apr 16 2020
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