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.
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, 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, 0, 19, 0, 0, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0
Offset: 1
Examples
The triangle begins:
k=1 2 3 4 5 6
n=1: 2;
n=2: 3, 0;
n=3: 0, 5, 0;
n=4: 5, 0, 7, 0;
n=5: 0, 7, 0, 0, 0;
n=6: 7, 0, 0, 0, 11, 0;
and so on.
Programs
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Mathematica
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 *)
Comments