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

1,1

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,...).

Links

Table of n, a(n) for n=1..78.

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.

Example

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.

Mathematica

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

Crossrefs

Cf. A005171, A062298, A052284, A157424

Sequence in context: A145273 A295892 A120522 * A098033 A284471 A135022

Adjacent sequences: A157420 A157421 A157422 * A157424 A157425 A157426

Keyword

nonn,tabl

Author

Gary W. Adamson & Mats Granvik, Feb 28 2009

Status

approved