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

0,8

Links

Table of n, a(n) for n=0..90.

Formula

A(n, k) = A010888(A004247(n, k)).

A(n, k) = A010888(A003991(n, k)) for n*k > 0.

Example

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, ...
    ...

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}]]

Prog

(PARI) T(n, k) = if (n && k, (n*k-1)%9+1, 0); \\ Michel Marcus, May 12 2022

Crossrefs

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).

Sequence in context: A048720 A067138 A059692 * A336225 A004247 A271916

Adjacent sequences: A353106 A353107 A353108 * A353110 A353111 A353112

Keyword

nonn,tabl,base,easy

Author

Stefano Spezia, Apr 24 2022

Status

approved