A336582 Numbers k with a Goldbach partition (p,q) such that k | (p*q - 1).

5, 10, 50, 58, 74, 106, 130, 170, 410, 562, 730, 850, 986, 1490, 1546, 1586, 2210, 2378, 2474, 2554, 2570, 2578, 3034, 3394, 3418, 3754, 3770, 4082, 4234, 4282, 4330, 4490, 4514, 5122, 5410, 5986, 6170, 6242, 6290, 6410, 6602, 6610, 7330, 7570, 7618, 7786, 8090, 8410, 8578, 9266, 9434

Offset

1,1

Comments

5 is the only odd term. See A335495.

Except for 5, k == +/- 2 (mod 12) & k == {2, 10} (mod 24).

A335495 = A336582 U A336583.

Links

Table of n, a(n) for n=1..51.

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

5 is in the sequence since it has a Goldbach partition, (3,2) such that 5 | (3*2 - 1) = 5;
10 is in the sequence since it has a Goldbach partition, (3,7) such that 10 | (3*7 - 1) = 20;
50 is in the sequence since it has a Goldbach partition, (7,43) such that 50 | (7*43 - 1) = 300;
58 is in the sequence since it has a Goldbach partition, (17,41) such that 58 | (17*41 - 1) = 696 = 58*12; etc.

Mathematica

fQ[n_] := Block[{p = 3}, While[ 2p +1 < n, q = n - p; If[ PrimeQ[q] && Mod[p*q, n] == 1, Goto[fini]]; p = NextPrime@ p]; Label[fini]; 2p +1 < n]; Select[Range@ 300, fQ]

Crossrefs

Cf. A335495, A336583, A336584.

Sequence in context: A216390 A305476 A270089 * A271275 A270100 A271287

Adjacent sequences: A336579 A336580 A336581 * A336583 A336584 A336585

Keyword

nonn

Author

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

Status

approved