A352169 - OEIS

%I #9 Feb 16 2025 08:34:03

%S 8,10,12,16,20,24,30,36,40,42,48,50,52,56,58,60,64,66,70,72,74,80,84,

%T 90,96,106,112,120,128,130,132,144,156,160,168,170,176,180,184,192,

%U 198,204,210,216,220,222,224,228,232,234,240,244,246,252,260,264,276,280,288,294,296

%N Numbers k with a Goldbach partition (p,q) such that k/2 divides at least one of p*q +- 1.

%H Eric Weisstein's World of Mathematics, <a href="https://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 20 is in the sequence since it has a Goldbach partition, namely (3,17), such that 20/2 = 10 | 3*17-1 = 50.

%o (PARI) isok(k) = if (!(k%2), my(q); forprime(p=2, k, if (isprime(q=k-p), if (!((p*q-1) % (k/2)) || !((p*q+1) % (k/2)), return(1))))); \\ _Michel Marcus_, Mar 07 2022

%Y Cf. A335495, A336582, A336583, A336584, A343797.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Mar 06 2022