The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A334065 Total area of all triangles such that p + q = 2*n, p < q (p, q prime), with base (q + p) and height (q - p). 0
 0, 0, 0, 8, 20, 12, 56, 128, 108, 200, 308, 312, 416, 336, 420, 512, 1088, 1080, 456, 1160, 1512, 1892, 2024, 2928, 2900, 2028, 3456, 2744, 3132, 4320, 2480, 6464, 6732, 2040, 6440, 7776, 6956, 8588, 11388, 6720, 8036, 13272, 11180, 7392, 16920, 10856, 10152, 16032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Eric Weisstein's World of Mathematics, Goldbach Partition Wikipedia, Goldbach's conjecture FORMULA a(n) = 2*n * Sum_{i=1..n} (n-i) * c(i) * c(2*n-i), where c is the prime characteristic (A010051). EXAMPLE a(4) = 8; 2*4 = 8 has one Goldbach partition: (5,3). The area of the triangle is (5 + 3)*(5 - 3)/2 = 8. a(8) = 128; 2*8 = 16 has the two Goldbach partitions: (13,3) and (11,5). The total area of the two triangles is (13 + 3)*(13 - 3)/2 + (11 + 5)*(11 - 5)/2 = 80 + 48 = 128. MATHEMATICA Table[2 n*Sum[(n - i) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n}], {n, 80}] PROG (PARI) a(n) = my(s=0); forprime(p=1, n, if (isprime(2*n-p), s+=n-p)); 2*n*s; \\ Michel Marcus, Apr 14 2020 CROSSREFS Cf. A010051. Sequence in context: A288423 A081963 A208085 * A128909 A115147 A302241 Adjacent sequences:  A334062 A334063 A334064 * A334066 A334067 A334068 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 13 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 03:57 EDT 2020. Contains 337264 sequences. (Running on oeis4.)