A352169 Numbers k with a Goldbach partition (p,q) such that k/2 divides at least one of p*q +- 1.

8, 10, 12, 16, 20, 24, 30, 36, 40, 42, 48, 50, 52, 56, 58, 60, 64, 66, 70, 72, 74, 80, 84, 90, 96, 106, 112, 120, 128, 130, 132, 144, 156, 160, 168, 170, 176, 180, 184, 192, 198, 204, 210, 216, 220, 222, 224, 228, 232, 234, 240, 244, 246, 252, 260, 264, 276, 280, 288, 294, 296

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Eric Weisstein's World of Mathematics, Goldbach Partition.

Wikipedia, Goldbach's conjecture.

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

Example

20 is in the sequence since it has a Goldbach partition, namely (3,17), such that 20/2 = 10 | 3*17-1 = 50.

Prog

(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

Crossrefs

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

Sequence in context: A154786 A335013 A249628 * A158273 A157939 A208154

Adjacent sequences: A352166 A352167 A352168 * A352170 A352171 A352172

Keyword

nonn

Author

Wesley Ivan Hurt, Mar 06 2022

Status

approved