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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.

%I A305883 #22 Feb 16 2025 08:33:54
%S A305883 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 A305883 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 A305883 23,5,31,7,29,13,23,17,19,7,31,3,37,11,29,17,23,5,37,11,31
%N 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.
%H A305883 Seiichi Manyama, <a href="/A305883/b305883.txt">Rows n = 4..374, flattened</a>
%H A305883 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A305883 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%e A305883   n  | (p,q)
%e A305883   ---+----------------------------
%e A305883    4 | (3,  5);
%e A305883    5 | (3,  7);
%e A305883    6 | (5,  7);
%e A305883    7 | (3, 11);
%e A305883    8 | (3, 13), (5, 11);
%e A305883    9 | (5, 13), (7, 11);
%e A305883   10 | (3, 17), (7, 13);
%e A305883   11 | (3, 19), (5, 17);
%e A305883   12 | (5, 19), (7, 17), (11, 13);
%t A305883 row[n_] := Select[Table[{p, 2 n - p}, {p, Prime[Range[PrimePi[n]]]}], Less @@ # && AllTrue[#, PrimeQ]&] // Union;
%t A305883 Table[row[n], {n, 4, 25}] // Flatten (* _Jean-François Alcover_, Jun 16 2018 *)
%Y A305883 Cf. A002373, A020481, A061357 (the size of row n), A078496, A078587.
%K A305883 nonn,tabf,look
%O A305883 4,1
%A A305883 _Seiichi Manyama_, Jun 13 2018