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%I #5 Jun 05 2021 14:23:08
%S 2,10,14,16,18,20,28,32,34,36,38,42,46,50,58,60,66,68,72,80,84,88,92,
%T 100,102,106,108,110,114,116,118,120,122,126,134,138,142,146,150,152,
%U 154,160,162,166,172,180,182,184,190,200,204,212,214,228,240,242,246,248,252,256,258
%N Positive even integers with an even number of Goldbach partitions.
%C This sequence is vacuously true for 2 since it has 0 Goldbach partitions.
%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 36 is in the sequence since it is a positive even integer with an even number of Goldbach partitions: (31,5), (29,7), (23,13), and (19,17).
%t Table[If[Mod[Sum[(PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1]), {k, n}], 2] == 0, 2 n, {}], {n, 200}] // Flatten
%Y Cf. A045917, A345016.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Jun 05 2021
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