A345017 Positive even integers with an even number of Goldbach partitions.

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.

Links

Table of n, a(n) for n=1..61.

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

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

Cf. A045917, A345016.

Sequence in context: A277087 A098735 A324856 * A349832 A050546 A032384

Adjacent sequences: A345014 A345015 A345016 * A345018 A345019 A345020

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 05 2021

Status

approved