login
A345017
Positive even integers with an even number of Goldbach partitions.
1
2, 10, 14, 16, 18, 20, 28, 32, 34, 36, 38, 42, 46, 50, 58, 60, 66, 68, 72, 80, 84, 88, 92, 100, 102, 106, 108, 110, 114, 116, 118, 120, 122, 126, 134, 138, 142, 146, 150, 152, 154, 160, 162, 166, 172, 180, 182, 184, 190, 200, 204, 212, 214, 228, 240, 242, 246, 248, 252, 256, 258
OFFSET
1,1
COMMENTS
This sequence is vacuously true for 2 since it has 0 Goldbach partitions.
EXAMPLE
36 is in the sequence since it is a positive even integer with an even number of Goldbach partitions: (31,5), (29,7), (23,13), and (19,17).
MATHEMATICA
Table[If[Mod[Sum[(PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1]), {k, n}], 2] == 0, 2 n, {}], {n, 200}] // Flatten
CROSSREFS
Sequence in context: A277087 A098735 A324856 * A349832 A050546 A032384
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 05 2021
STATUS
approved