login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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