A157423 Triangle read by rows, T(n,k) = 0 if (n-k+1) is prime, else 1.

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

Offset: 1

Author

Gary W. Adamson & Mats Granvik, Feb 28 2009

Keywords

• nonn
• tabl

Comments

Row sums = A062298: (1, 1, 1, 2, 2, 3, 3, 4, 5, 6,...). Eigensequence of the triangle = A052284: (1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...).

Examples

			First few rows of the triangle =
1;
0, 1;
0, 0, 1;
1, 0, 0, 1;
0, 1, 0, 0, 1;
1, 0, 1, 0, 0, 1;
0, 1, 0, 1, 0, 0, 1;
1, 0, 1, 0, 1, 0, 0, 1;
1, 1, 0, 1, 0, 1, 0, 0, 1;
1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
...
Example: T(6,4) = 0 since (6 - 4 + 1) = 3, prime.
		

Crossrefs

Cf. A005171, A062298, A052284, A157424

Programs

Mathematica

Table[If[PrimeQ[n-k+1],0,1],{n,15},{k,n}]//Flatten (* Harvey P. Dale, Jul 19 2016 *)

Formula

Triangle read by rows, T(n,k) = 0 if (n-k+1) is prime, else 1. By columns, A005171 in every column: where A005171(k) = 0 if k is prime.