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%I #13 Aug 22 2020 13:10:45
%S 8,12,24,30,36,40,42,48,56,60,66,70,72,84,90,96,112,120,132,144,156,
%T 168,180,184,198,204,210,216,220,222,224,228,232,234,240,246,252,260,
%U 264,276,280,288,294,296,300,304,312,318,330,336,340,360,372,374,380,384,390
%N Numbers k with a Goldbach partition (p,q) such that k | (p*q + 1).
%C k is even.
%C A335495 = A336582 U A336583.
%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 8 is in the sequence since it has a Goldbach partition, (5,3) such that 8 | (3*5 + 1) = 16;
%e 12 is in the sequence since it has a Goldbach partition, (7,5) such that 12 | (5*7 + 1) = 36;
%e 42 is in the sequence since it has a Goldbach partition, (13,29) such that 42 | (13*29 + 1) = 378 = 9*42; etc.
%t fQ[n_] := Block[{p = 3, q}, While[q = n - p; m = Mod[p*q, n] + 1; p < q && ! PrimeQ@q || m != n, p = NextPrime@p]; p < q]; Select[2 Range@200, fQ]
%Y Cf. A335495, A336582, A336584.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_ and _Robert G. Wilson v_, Jul 26 2020
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