

A336582


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


3



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
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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



