A334160 Even numbers with a Goldbach partition (p,q), p < q, such that p and q can be written as the sum of two primes.

12, 18, 20, 24, 26, 32, 36, 38, 44, 48, 50, 56, 62, 66, 68, 74, 78, 80, 86, 92, 104, 108, 110, 114, 116, 122, 128, 134, 140, 144, 146, 152, 156, 158, 164, 170, 176, 182, 186, 188, 194, 198, 200, 204, 206, 212, 218, 224, 230, 234, 236, 242, 246, 248, 254, 260, 266

Offset

1,1

Comments

All terms == 0 or 2 (mod 6). Those == 0 (mod 6) are 5 + A006512(k) for k > 1. - Robert Israel, May 28 2026

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

12 is in the sequence since 12 = 7 + 5 (distinct primes), 7 = 5 + 2 (both prime) and 5 = 3 + 2 (both prime).
18 is in the sequence since 18 = 13 + 5 (distinct primes), 13 = 11 + 2 (both prime) and 5 = 3 + 2 (both prime).

Maple

N:= 500: # for terms <= N
P:= select(t -> isprime(t) and isprime(t-2), [5, seq(i, i=7..N, 6)]):
sort(convert(select(`<=`, {seq(seq(P[i]+P[j], i=1..j-1), j=1..nops(P))}, N), list)); # Robert Israel, May 28 2026

Mathematica

Table[If[Sum[(PrimePi[i - 2] - PrimePi[i - 3]) (PrimePi[2 n - i - 2] - PrimePi[2 n - i - 3]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n - 1}] > 0, 2 n, {}], {n, 150}] // Flatten

Crossrefs

Cf. A006512, A396487.

Sequence in context: A025491 A091196 A319229 * A396487 A271345 A007624

Adjacent sequences: A334157 A334158 A334159 * A334161 A334162 A334163

Keyword

nonn,easy,changed

Author

Wesley Ivan Hurt, Apr 16 2020

Status

approved