A118683 Triangle, T(n,k) = A039701(n) + A039701(k) - A039701(n)*A039701(k), read by rows.

0, 2, 0, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Roger L. Bagula, May 19 2006

Keywords

• nonn
• tabl
• less
• easy

Examples

			Triangle begins as:
  0;
  2, 0;
  0, 2, 0;
  1, 1, 1, 1;
  0, 2, 0, 1, 0;
  1, 1, 1, 1, 1, 1;
  0, 2, 0, 1, 0, 1, 0;
  1, 1, 1, 1, 1, 1, 1, 1;
  0, 2, 0, 1, 0, 1, 0, 1, 0;
  0, 2, 0, 1, 0, 1, 0, 1, 0, 0;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A039701, A099618 (right diagonal).

Programs

Magma

A039701:= func< n | NthPrime(n) mod 3 >;
A118683:= func< n,k | A039701(n)+A039701(k)-A039701(n)*A039701(k) >;
[A118683(n,k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 01 2024

Mathematica

A039701[n_]:= Mod[Prime[n],3];
T[n_, k_]:= A039701[n] +A039701[k] -A039701[n]*A039701[k];
Table[T[n,k], {n,12}, {k,n}]//Flatten

SageMath

def A039701(n): return nth_prime(n)%3
def A118683(n,k): return A039701(n)+A039701(k)-A039701(n)*A039701(n)
flatten([[A039701(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Apr 01 2024

Extensions

Offset corrected, definition clarified, sequence extended by Assoc. Eds. of the OEIS, Jun 15 2010