A342955 Array T(n,k), n, k >= 0, read by antidiagonals; the i-th decimal digit of T(n, k) is the smallest of the i-th digits of n and of k.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 0, 2, 3, 4, 5, 5, 4, 3, 2, 0, 0, 0, 1, 0, 3, 4, 5, 6, 5, 4, 3, 0, 1, 0

Offset: 0

Author

Rémy Sigrist, Apr 03 2021

Keywords

• nonn
• tabl
• base
• easy
• look

Comments

This sequence has similarities with lunar addition (A087061); here we take the smallest, there the largest digits. It is "lunar multiplication" of corresponding digits.

The bitwise AND operator (A004198) is the binary analog.

Examples

			Array T(n, k) begins:
  n\k|  0  1  2  3  4  5  6  7  8  9  10  11  12  13
  ---+----------------------------------------------
    0|  0  0  0  0  0  0  0  0  0  0   0   0   0   0
    1|  0  1  1  1  1  1  1  1  1  1   0   1   1   1
    2|  0  1  2  2  2  2  2  2  2  2   0   1   2   2
    3|  0  1  2  3  3  3  3  3  3  3   0   1   2   3
    4|  0  1  2  3  4  4  4  4  4  4   0   1   2   3
    5|  0  1  2  3  4  5  5  5  5  5   0   1   2   3
    6|  0  1  2  3  4  5  6  6  6  6   0   1   2   3
    7|  0  1  2  3  4  5  6  7  7  7   0   1   2   3
    8|  0  1  2  3  4  5  6  7  8  8   0   1   2   3
    9|  0  1  2  3  4  5  6  7  8  9   0   1   2   3
   10|  0  0  0  0  0  0  0  0  0  0  10  10  10  10
   11|  0  1  1  1  1  1  1  1  1  1  10  11  11  11
   12|  0  1  2  2  2  2  2  2  2  2  10  11  12  12
   13|  0  1  2  3  3  3  3  3  3  3  10  11  12  13
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010
• Rémy Sigrist, Colored representation of the array for n, k < 1000 (where the color is function of T(n, k))

Crossrefs

Cf. A004197 (numerical minimum), A004198 (bitwise minimum), A087061 (digit-wise maximum).

Programs

PARI

T(n,k,base=10) = if (n==0 || k==0, 0, T(n\base,k\base)*base + min(n%base, k%base))

Formula

T(n, k) = T(k, n).

T(m, T(n, k)) = T(T(m, n), k).

T(n, n) = n.

T(n, 0) = 0.

T(n, k) + A087061(n, k) = n + k.