OFFSET
1,5
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
EXAMPLE
a(13) = 4; The Goldbach partitions of A352240(13) = 60 are: 7+53 = 13+47 = 17+43 = 19+41 = 23+37 = 29+31. The 4 pairs of Goldbach partitions of 60 that are being counted are: (13,47),(17,43); (17,43),(19,41); (19,41),(23,37); and (23,37),(29,31). Note that the pair (7,53),(13,47) is not counted since there is a prime in the interval (7,13), namely 11.
MATHEMATICA
a[n_] := 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}];
Table[If[a[n] > 0, a[n], {}], {n, 100}] // Flatten
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Mar 09 2022
STATUS
approved