OFFSET
1,1
COMMENTS
Similar to A187797 but also contains the numbers 82, 96, 98, 110, 136, ...
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
EXAMPLE
82 is in the sequence since it has at least one pair of Goldbach partitions, namely (23,59) and (29,53), such that all integers in the open intervals (23,29) and (53,59) are composite.
MATHEMATICA
Table[If[Sum[Sum[KroneckerDelta[NextPrime[k], i]*KroneckerDelta[NextPrime[2 n - i], 2 n - k]*(PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {k, i}], {i, n}] > 0, 2 n, {}], {n, 150}] // Flatten
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Mar 08 2022
STATUS
approved