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 A345016 Positive even integers with an odd number of Goldbach partitions. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 22 20:45 EDT 2024. Contains 372758 sequences. (Running on oeis4.)