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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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..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

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

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)