A336583 Numbers k with a Goldbach partition (p,q) such that k | (p*q + 1).

8, 12, 24, 30, 36, 40, 42, 48, 56, 60, 66, 70, 72, 84, 90, 96, 112, 120, 132, 144, 156, 168, 180, 184, 198, 204, 210, 216, 220, 222, 224, 228, 232, 234, 240, 246, 252, 260, 264, 276, 280, 288, 294, 296, 300, 304, 312, 318, 330, 336, 340, 360, 372, 374, 380, 384, 390

Offset

1,1

Comments

k is even.

A335495 = A336582 U A336583.

Links

Table of n, a(n) for n=1..57.

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

8 is in the sequence since it has a Goldbach partition, (5,3) such that 8 | (3*5 + 1) = 16;
12 is in the sequence since it has a Goldbach partition, (7,5) such that 12 | (5*7 + 1) = 36;
42 is in the sequence since it has a Goldbach partition, (13,29) such that 42 | (13*29 + 1) = 378 = 9*42; etc.

Mathematica

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]

Crossrefs

Cf. A335495, A336582, A336584.

Sequence in context: A326994 A367146 A278902 * A333754 A088525 A054735

Adjacent sequences: A336580 A336581 A336582 * A336584 A336585 A336586

Keyword

nonn

Author

Wesley Ivan Hurt and Robert G. Wilson v, Jul 26 2020

Status

approved