A353109 Array read by antidiagonals: A(n, k) is the digital root of n*k with n >= 0 and k >= 0.
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 4, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 9, 8, 5, 0, 0, 6, 1, 3, 3, 1, 6, 0, 0, 7, 3, 6, 7, 6, 3, 7, 0, 0, 8, 5, 9, 2, 2, 9, 5, 8, 0, 0, 9, 7, 3, 6, 7, 6, 3, 7, 9, 0, 0, 1, 9, 6, 1, 3, 3, 1, 6, 9, 1, 0, 0, 2, 2, 9, 5, 8, 9, 8, 5, 9, 2, 2, 0
Offset: 0
Examples
The array begins:
0, 0, 0, 0, 0, 0, 0, 0, ...
0, 1, 2, 3, 4, 5, 6, 7, ...
0, 2, 4, 6, 8, 1, 3, 5, ...
0, 3, 6, 9, 3, 6, 9, 3, ...
0, 4, 8, 3, 7, 2, 6, 1, ...
0, 5, 1, 6, 2, 7, 3, 8, ...
0, 6, 3, 9, 6, 3, 9, 6, ...
0, 7, 5, 3, 1, 8, 6, 4, ...
...
Crossrefs
Programs
-
Mathematica
A[i_,j_]:=If[i*j==0,0,1+Mod[i*j-1,9]];Flatten[Table[A[n-k,k],{n,0,12},{k,0,n}]] -
PARI
T(n,k) = if (n && k, (n*k-1)%9+1, 0); \\ Michel Marcus, May 12 2022