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

1,1

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.

Links

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

Formula

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

Example

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;
...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A164056 A286059 A163539 * A242018 A324682 A288132

Adjacent sequences: A143535 A143536 A143537 * A143539 A143540 A143541

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 23 2008

Status

approved