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A353109
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Array read by antidiagonals: A(n, k) is the digital root of n*k with n >= 0 and k >= 0.
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6
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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
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OFFSET
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0,8
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LINKS
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FORMULA
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EXAMPLE
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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, ...
...
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MATHEMATICA
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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}]]
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PROG
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(PARI) T(n, k) = if (n && k, (n*k-1)%9+1, 0); \\ Michel Marcus, May 12 2022
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CROSSREFS
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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).
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KEYWORD
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AUTHOR
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STATUS
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approved
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