A333998 Positive even integers 2k such that for all Goldbach partitions (p,q) of 2k, there exists a prime r_0 in p < r_0 < q.

2, 16, 20, 28, 32, 40, 44, 48, 50, 54, 56, 64, 66, 70, 72, 76, 80, 88, 92, 96, 98, 102, 104, 108, 110, 114, 116, 124, 126, 130, 132, 136, 140, 148, 150, 154, 156, 160, 164, 168, 170, 174, 176, 180, 182, 184, 188, 190, 192, 196, 200, 208, 212, 220, 224, 228, 230

Offset

1,1

Links

Table of n, a(n) for n=1..57.

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

Mathematica

Flatten[Table[If[1 - PrimePi[n] + PrimePi[n - 1] - Sum[KroneckerDelta[PrimePi[i] + 1, PrimePi[2 n - i]] (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n}] > 0, 2 n, {}], {n, 100}]]

Crossrefs

Cf. A002375.

Sequence in context: A323193 A050850 A082475 * A081767 A093026 A271627

Adjacent sequences: A333995 A333996 A333997 * A333999 A334000 A334001

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 11 2020

Status

approved