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%I #21 Jun 02 2022 17:48:03
%S 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,
%T 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,
%U 9,6,1,3,3,1,6,9,1,0,0,2,2,9,5,8,9,8,5,9,2,2,0
%N Array read by antidiagonals: A(n, k) is the digital root of n*k with n >= 0 and k >= 0.
%F A(n, k) = A010888(A004247(n, k)).
%F A(n, k) = A010888(A003991(n, k)) for n*k > 0.
%e The array begins:
%e 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 2, 3, 4, 5, 6, 7, ...
%e 0, 2, 4, 6, 8, 1, 3, 5, ...
%e 0, 3, 6, 9, 3, 6, 9, 3, ...
%e 0, 4, 8, 3, 7, 2, 6, 1, ...
%e 0, 5, 1, 6, 2, 7, 3, 8, ...
%e 0, 6, 3, 9, 6, 3, 9, 6, ...
%e 0, 7, 5, 3, 1, 8, 6, 4, ...
%e ...
%t 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}]]
%o (PARI) T(n,k) = if (n && k, (n*k-1)%9+1, 0); \\ _Michel Marcus_, May 12 2022
%Y Cf. A003991, A004247, A010888, A056992 (diagonal), A073636, A139413, A180592, A180593, A180594, A180595, A180596, A180597, A180598, A180599, A303296, A336225, A353128 (antidiagonal sums), A353933, A353974 (partial sum of the main diagonal).
%K nonn,tabl,base,easy
%O 0,8
%A _Stefano Spezia_, Apr 24 2022
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