A305883 - OEIS

%I #21 Jun 24 2018 11:59:18

%S 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,

%T 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,

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

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

%H Seiichi Manyama, <a href="/A305883/b305883.txt">Rows n = 4..374, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%e   n  | (p,q)

%e   ---+----------------------------

%e    4 | (3,  5);

%e    5 | (3,  7);

%e    6 | (5,  7);

%e    7 | (3, 11);

%e    8 | (3, 13), (5, 11);

%e    9 | (5, 13), (7, 11);

%e   10 | (3, 17), (7, 13);

%e   11 | (3, 19), (5, 17);

%e   12 | (5, 19), (7, 17), (11, 13);

%t row[n_] := Select[Table[{p, 2 n - p}, {p, Prime[Range[PrimePi[n]]]}], Less @@ # && AllTrue[#, PrimeQ]&] // Union;

%t Table[row[n], {n, 4, 25}] // Flatten (* _Jean-François Alcover_, Jun 16 2018 *)

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

%K nonn,tabf,look

%O 4,1

%A _Seiichi Manyama_, Jun 13 2018