|
|
A336582
|
|
Numbers k with a Goldbach partition (p,q) such that k | (p*q - 1).
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
5 is the only odd term. See A335495.
Except for 5, k == +/- 2 (mod 12) & k == {2, 10} (mod 24).
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|