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

0,1

Links

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

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).

Example

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;

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

Prog

(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

Crossrefs

Cf. A106727.

Sequence in context: A271369 A308322 A308898 * A292603 A308880 A319047

Adjacent sequences: A106725 A106726 A106727 * A106729 A106730 A106731

Keyword

nonn,tabl,easy,less

Author

Roger L. Bagula, May 14 2005

Extensions

Edited by G. C. Greubel, Sep 10 2021

Status

approved