A305883 Triangle read by rows: row n lists the pairs (p, q) such that p, q are primes, p+q=2*n and p < q.

3, 5, 3, 7, 5, 7, 3, 11, 3, 13, 5, 11, 5, 13, 7, 11, 3, 17, 7, 13, 3, 19, 5, 17, 5, 19, 7, 17, 11, 13, 3, 23, 7, 19, 5, 23, 11, 17, 7, 23, 11, 19, 13, 17, 3, 29, 13, 19, 3, 31, 5, 29, 11, 23, 5, 31, 7, 29, 13, 23, 17, 19, 7, 31, 3, 37, 11, 29, 17, 23, 5, 37, 11, 31

Offset: 4

Author

Seiichi Manyama, Jun 13 2018

Keywords

• nonn
• tabf
• look

Examples

			  n  | (p,q)
  ---+----------------------------
   4 | (3,  5);
   5 | (3,  7);
   6 | (5,  7);
   7 | (3, 11);
   8 | (3, 13), (5, 11);
   9 | (5, 13), (7, 11);
  10 | (3, 17), (7, 13);
  11 | (3, 19), (5, 17);
  12 | (5, 19), (7, 17), (11, 13);
		

Links

• Seiichi Manyama, Rows n = 4..374, flattened
• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture

Crossrefs

Cf. A002373, A020481, A061357 (the size of row n), A078496, A078587.

Programs

Mathematica

row[n_] := Select[Table[{p, 2 n - p}, {p, Prime[Range[PrimePi[n]]]}], Less @@ # && AllTrue[#, PrimeQ]&] // Union;
Table[row[n], {n, 4, 25}] // Flatten (* Jean-François Alcover, Jun 16 2018 *)