A106728 Triangle T(n, k) = ( ((f(n+1) mod 5) mod 4) + ((f(k+1) mod 5) mod 4) ) mod 4, where f(n) = 10 - (prime(n+3) mod 10).

2, 3, 0, 1, 2, 0, 2, 3, 1, 2, 0, 1, 3, 0, 2, 1, 2, 0, 1, 3, 0, 0, 1, 3, 0, 2, 3, 2, 3, 0, 2, 3, 1, 2, 1, 0, 2, 3, 1, 2, 0, 1, 0, 3, 2, 3, 0, 2, 3, 1, 2, 1, 0, 3, 0, 1, 2, 0, 1, 3, 0, 3, 2, 1, 2, 0, 2, 3, 1, 2, 0, 1, 0, 3, 2, 3, 1, 2, 1, 2, 0, 1, 3, 0, 3, 2, 1, 2, 0, 1, 0, 0, 1, 3, 0, 2, 3, 2, 1, 0, 1, 3, 0, 3, 2

Offset: 0

Author

Roger L. Bagula, May 14 2005

Keywords

• nonn
• tabl
• easy
• less

Examples

			Triangle begins as:
  2;
  3, 0;
  1, 2, 0;
  2, 3, 1, 2;
  0, 1, 3, 0, 2;
  1, 2, 0, 1, 3, 0;
  0, 1, 3, 0, 2, 3, 2;
  3, 0, 2, 3, 1, 2, 1, 0;
  2, 3, 1, 2, 0, 1, 0, 3, 2;
  3, 0, 2, 3, 1, 2, 1, 0, 3, 0;
  1, 2, 0, 1, 3, 0, 3, 2, 1, 2, 0;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A106727.

Programs

Mathematica

f[n_]= 10 -Mod[Prime[n+3], 10];
T[n_, k_]:= Mod[Mod[Mod[f[n+1], 5], 4] + Mod[Mod[f[k+1], 5], 4], 4];
Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten

Sage

def f(n): return 10 - (nth_prime(n+3)%10)
def A106728(n,k): return ( ((f(n+1))%5)%4 + ((f(k+1))%5)%4 )%4
flatten([[A106728(n,k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Sep 10 2021

Formula

T(n, k) = ( ((f(n+1) mod 5) mod 4) + ((f(k+1) mod 5) mod 4) ) mod 4, where f(n) = 10 - (prime(n+3) mod 10).

Extensions

Edited by G. C. Greubel, Sep 10 2021