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Triangle read by rows: T(n,k) = 1 if n+k is a prime, otherwise T(n,k) = 0; n >= 1, k >= 1.
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%I #48 Aug 12 2022 11:41:36

%S 1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,1,0,

%T 0,0,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,

%U 0,0,1,0,1,0,0,0,1,0,0,0,0,1,0,1

%N Triangle read by rows: T(n,k) = 1 if n+k is a prime, otherwise T(n,k) = 0; n >= 1, k >= 1.

%C Row sums see A108954.

%F T(n,k) = A057427(A353612(n,k)) = signum(A353612(n,k)).

%F T(n-k,k) = A010051(n).

%e The triangle begins:

%e k=1 2 3 4 5 6

%e n=1: 1;

%e n=2: 1, 0;

%e n=3: 0, 1, 0;

%e n=4: 1, 0, 1, 0;

%e n=5: 0, 1, 0, 0, 0;

%e n=6: 1, 0, 0, 0, 1, 0;

%e and so on.

%t T[n_, k_] := If[PrimeQ[n + k], 1, 0]; Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Jul 21 2022 *)

%Y Cf. A000040, A010051, A057427, A108954, A353612.

%K nonn,tabl

%O 1

%A _Ctibor O. Zizka_, Jul 21 2022