This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A353612 #39 Jul 21 2022 10:46:49
%S A353612 2,3,0,0,5,0,5,0,7,0,0,7,0,0,0,7,0,0,0,11,0,0,0,0,11,0,13,0,0,0,11,0,
%T A353612 13,0,0,0,0,11,0,13,0,0,0,17,0,11,0,13,0,0,0,17,0,19,0,0,13,0,0,0,17,
%U A353612 0,19,0,0,0,13,0,0,0,17,0,19,0,0,0,23,0
%N A353612 Triangle read by rows: T(n,k) = (n + k) if (n + k) is a prime number, otherwise T(n,k) = 0; n >= 1, k >= 1.
%C A353612 Row sums see A341700.
%e A353612 The triangle begins:
%e A353612 k=1 2 3 4 5 6
%e A353612 n=1: 2;
%e A353612 n=2: 3, 0;
%e A353612 n=3: 0, 5, 0;
%e A353612 n=4: 5, 0, 7, 0;
%e A353612 n=5: 0, 7, 0, 0, 0;
%e A353612 n=6: 7, 0, 0, 0, 11, 0;
%e A353612 and so on.
%t A353612 T[n_, k_] := If[PrimeQ[n + k], n + k, 0]; Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Jul 21 2022 *)
%Y A353612 Cf. A000040, A341700.
%K A353612 nonn,tabl
%O A353612 1,1
%A A353612 _Ctibor O. Zizka_, Jul 21 2022