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A279728
Sum of the larger parts of the Goldbach partitions (p,q) of 2n such that all primes from p to q (inclusive) appear as a part in some Goldbach partition of p+q = 2n.
5
0, 0, 3, 5, 12, 7, 7, 0, 24, 0, 11, 49, 13, 0, 59, 0, 17, 42, 19, 0, 23, 0, 23, 0, 0, 29, 0, 0, 29, 199, 31, 0, 0, 37, 0, 0, 37, 0, 41, 0, 41, 143, 43, 0, 47, 0, 47, 0, 0, 53, 0, 0, 112, 0, 0, 59, 0, 0, 59, 128, 61, 0, 0, 67, 0, 0, 67, 0, 71, 0, 71, 73, 73, 0, 0, 79, 0, 0
OFFSET
1,3
FORMULA
a(n) = Sum_{i=3..n} ((2n-i) * c(i) * c(2n-i) * (Product_{k=i..n} (1-abs(c(k) - c(2n-k))))), where c = A010051.
MAPLE
with(numtheory): A279728:=n->add( (2*n-i) * (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*n-k)-pi(2*n-k-1))), k=i..n)), i=3..n): seq(A279728(n), n=1..100);
MATHEMATICA
Table[Sum[((2 n - i) Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]]) Product[1 - Abs[Boole[PrimeQ@ k] - Boole[PrimeQ[2 n - k]]], {k, i, n}], {i, 3, n}], {n, 100}] (* Michael De Vlieger, Dec 18 2016 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Wesley Ivan Hurt, Dec 17 2016
STATUS
approved