A143541 Triangle read by rows, T(n,k) = 1 if both n and k are prime, 0 otherwise; 1 <= k <= n.

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

Offset

1,1

Comments

Row sums = A049084.

The n-th row = n zeros if n is a nonprime; first n terms of A010051 (the characteristic function of primes) if n is prime.

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1275 (rows n=1..50).

Formula

T(n,k) = 1 if n and k are prime, 0 otherwise.

Example

First few rows of the triangle are:
  0;
  0, 1;
  0, 1, 1;
  0, 0, 0, 0;
  0, 1, 1, 0, 1;
  0, 0, 0, 0, 0, 0;
  0, 1, 1, 0, 1, 0, 1;
  ...
Row 5 = first 5 terms of A010051: (0, 1, 1, 0, 1).
T(5,3) = 1 since (5,3) are prime; but T(5,4) = 0 since 4 is a nonprime.

Maple

T:=(n, k)->`if`(isprime(n) and isprime(k), 1, 0): seq(seq(T(n, k), k=1..n), n=1..12); # Muniru A Asiru, Oct 28 2018

Mathematica

nn = 11; Flatten[Table[Table[If[And[PrimeQ[n], PrimeQ[k]], 1, 0], {k, 1, n}], {n, 1, nn}]] (* Mats Granvik, Oct 28 2018 *)

Prog

(PARI) row(n) = vector(n, k, isprime(n) && isprime(k)); \\ Michel Marcus, Mar 18 2026

Crossrefs

Cf. A010051, A049084.

Sequence in context: A288622 A095907 A056051 * A359583 A344120 A090173

Adjacent sequences: A143538 A143539 A143540 * A143542 A143543 A143544

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 23 2008

Status

approved