A353663 Triangle read by rows: T(n,k) = 1 if n+k is a prime, otherwise T(n,k) = 0; n >= 1, k >= 1.

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, 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, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1

Offset

1

Comments

Row sums see A108954.

Links

Table of n, a(n) for n=1..84.

Formula

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

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

Example

The triangle begins:
      k=1  2  3  4  5  6
  n=1:  1;
  n=2:  1, 0;
  n=3:  0, 1, 0;
  n=4:  1, 0, 1, 0;
  n=5:  0, 1, 0, 0, 0;
  n=6:  1, 0, 0, 0, 1, 0;
  and so on.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A365428 A156277 A359377 * A260595 A328102 A177444

Adjacent sequences: A353660 A353661 A353662 * A353664 A353665 A353666

Keyword

nonn,tabl

Author

Ctibor O. Zizka, Jul 21 2022

Status

approved