

A334119


Total area of all triangles such that p + q = 2*n, p < q (p, q prime), with base (q  p) and height q.


0



0, 0, 0, 5, 14, 7, 44, 98, 74, 158, 254, 231, 344, 258, 294, 434, 920, 856, 372, 959, 1180, 1613, 1772, 2357, 2438, 1689, 2696, 2303, 2610, 3318, 2168, 5549, 5538, 1758, 5324, 6366, 6146, 7355, 9610, 5628, 6830, 10940, 9962, 6180, 13524, 9320, 8748, 13015, 4308
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


LINKS

Table of n, a(n) for n=1..49.
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


FORMULA

a(n) = Sum_{i=1..n1} (ni) * (2*ni) * c(i) * c(2*ni), 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

Cf. A010051, A334079.
Sequence in context: A051542 A083660 A003079 * A205128 A292249 A205134
Adjacent sequences: A334116 A334117 A334118 * A334120 A334121 A334122


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 14 2020


STATUS

approved



