%I #72 Dec 05 2019 04:17:39
%S 0,3,3,5,6,5,7,8,8,7,0,10,10,10,0,11,3,12,12,3,11,13,14,5,14,5,14,13,
%T 0,16,16,7,7,16,16,0,17,3,18,18,0,18,18,3,17,19,20,5,20,11,11,20,5,20,
%U 19,0,22,22,7,13,22,13,7,22,22,0,23,3,24,24,0,24,24,0,24,24,3,23
%N Square array T(n,k) (n >= 1, k >= 1) read by antidiagonals: first row and column are A085090, other entries equal sum of entries in first row and first column.
%C This is related to Goldbach's conjecture, since entries for which the leftmost entry and the top entry are both nonzero are the sums of two primes.
%C The successive antidiagonals may also be regarded as the rows of a triangle, having A085090 as outside diagonals.
%H Gustavo Funes, Damian Gulich, Leopoldo Garavaglia and Mario Garavaglia, <a href="http://www.mi.sanu.ac.rs/vismath/garavaglia2008/index.html">Hidden Symmetries Among Primes</a>, Form and Symmetry: Art and Science, Buenos Aires Congress, 2007, Section 4, Figure 10.
%H Fred Daniel Kline, <a href="/A317745/a317745_3.pdf">Goldbach Illustrated</a>
%F T(n, k) = A085090(n) + A085090(k).
%e Beginning of the array. All elements are equal to topmost value plus leftmost value.
%e 0 3 5 7 0 11 13 0 17 19 0 23
%e 3 6 8 10 3 14 16 3 20 22 3
%e 5 8 10 12 5 16 18 5 22 24
%e 7 10 12 14 7 18 20 7 24
%e 0 3 5 7 0 11 13 0
%e 11 14 16 18 11 22 24
%e 13 16 18 20 13 24
%e 0 3 5 7 0
%e 17 20 22 24
%e 19 22 24
%e 0 3
%e 23
%t i[n_] := If[PrimeQ[2 n - 1], 2 n - 1, 0]; A085090 = Array[i, 82];
%t r[k_] := Table[A085090[[j]] + A085090[[k - j + 1]], {j, 1, k}];
%t a = Array[r, 12] // Flatten,
%o (PARI) a085090(n) = if (isprime(p=2*n-1), p, 0);
%o row(n) = vector(n, k, a085090(k) + a085090(n-k+1));
%o tabl(nn) = for (n=1, nn, print(row(n))); \\ _Michel Marcus_, Aug 09 2018
%Y Cf. A085090.
%K nonn,tabl
%O 1,2
%A _Fred Daniel Kline_, Aug 05 2018
%E Edited by _N. J. A. Sloane_, Sep 09 2018