A345016 Positive even integers with an odd number of Goldbach partitions.

4, 6, 8, 12, 22, 24, 26, 30, 40, 44, 48, 52, 54, 56, 62, 64, 70, 74, 76, 78, 82, 86, 90, 94, 96, 98, 104, 112, 124, 128, 130, 132, 136, 140, 144, 148, 156, 158, 164, 168, 170, 174, 176, 178, 186, 188, 192, 194, 196, 198, 202, 206, 208, 210, 216, 218, 220, 222, 224, 226, 230

Offset

1,1

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

24 is in the sequence since it is a positive even integer with an odd number of Goldbach partitions: (19,5), (17,7), and (13,11).

Mathematica

Table[If[Mod[Sum[(PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1]), {k, n}] + 1, 2] == 0, 2 n, {}], {n, 200}] // Flatten

Crossrefs

Cf. A045917, A345017.

Sequence in context: A323059 A136254 A146528 * A216051 A176777 A318761

Adjacent sequences: A345013 A345014 A345015 * A345017 A345018 A345019

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 05 2021

Status

approved