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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.
2
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
4,1
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
EXAMPLE
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);
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 *)
CROSSREFS
Cf. A002373, A020481, A061357 (the size of row n), A078496, A078587.
Sequence in context: A074593 A144294 A255313 * A154800 A263175 A137768
KEYWORD
nonn,tabf,look
AUTHOR
Seiichi Manyama, Jun 13 2018
STATUS
approved