A143538 Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n.

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

Offset: 1

Author

Gary W. Adamson, Aug 23 2008

Keywords

• nonn
• tabl

Comments

Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n. A000012 * (A010051 * 0^(n-k)). A010051 * 0^(n-k) = an infinite lower triangular matrix with A010051 (the characteristic function of the primes) as the main diagonal and the rest zeros. The multiplier A000012 takes partial sums of column terms.

Examples

			First few rows of the triangle =
0;
0, 1;
0, 1, 1;
0, 1, 1, 0;
0, 1, 1, 0, 1;
0, 1, 1, 0, 1, 0;
0, 1, 1, 0, 1, 0, 1;
...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Crossrefs

Cf. A000720 (row sums), A002260, A010051.

Programs

Mathematica

Table[If[PrimeQ[k], 1, 0], {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Sep 17 2017 *)

PARI

for(n=1,10, for(k=1,n, print1(if(isprime(k),1,0), ", "))) \\ G. C. Greubel, Sep 17 2017

Formula

a(n) = A010051(A002260(n)). - Wesley Ivan Hurt, Sep 20 2021