OFFSET
1,4
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
FORMULA
a(n) = Sum_{i=1..n-1} (n-i) * (2*n-i) * c(i) * c(2*n-i), where c is the prime characteristic (A010051).
EXAMPLE
a(4) = 5; 2*4 = 8 has one Goldbach partition: (5,3). The area of the triangle is (5 - 3)*5/2 = 5.
a(8) = 98; 2*8 = 16 has two Goldbach partitions: (13,3) and (11,5). The sum of the areas is (13 - 3)*13/2 + (11 - 5)*11/2 = 65 + 33 = 98.
MATHEMATICA
Table[Sum[(n - i) (2 n - i) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n - 1}], {n, 60}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 14 2020
STATUS
approved