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

0,13

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.

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))

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.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A359902 A111143 A356969 * A004197 A261684 A048571

Adjacent sequences: A342952 A342953 A342954 * A342956 A342957 A342958

Keyword

nonn,tabl,base,easy,look

Author

Rémy Sigrist, Apr 03 2021

Status

approved