A344837 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = min(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 4, 2, 2, 4, 0, 0, 4, 4, 3, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 5, 4, 5, 4, 4, 0, 0, 8, 4, 6, 4, 4, 6, 4, 8, 0, 0, 8, 8, 6, 4, 5, 4, 6, 8, 8, 0, 0, 8, 8, 8, 4, 5, 5, 4, 8, 8, 8, 0, 0, 8, 8, 9, 8, 5, 6, 5, 8, 9, 8, 8, 0

Offset: 0

Author

Rémy Sigrist, May 29 2021

Keywords

• nonn
• base
• tabl

Comments

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then take the least value.

Examples

			Array T(n, k) begins:
  n\k|  0  1  2   3  4   5   6   7  8  9  10  11  12  13  14  15
  ---+----------------------------------------------------------
    0|  0  0  0   0  0   0   0   0  0  0   0   0   0   0   0   0
    1|  0  1  2   2  4   4   4   4  8  8   8   8   8   8   8   8
    2|  0  2  2   2  4   4   4   4  8  8   8   8   8   8   8   8
    3|  0  2  2   3  4   5   6   6  8  9  10  11  12  12  12  12
    4|  0  4  4   4  4   4   4   4  8  8   8   8   8   8   8   8
    5|  0  4  4   5  4   5   5   5  8  9  10  10  10  10  10  10
    6|  0  4  4   6  4   5   6   6  8  9  10  11  12  12  12  12
    7|  0  4  4   6  4   5   6   7  8  9  10  11  12  13  14  14
    8|  0  8  8   8  8   8   8   8  8  8   8   8   8   8   8   8
    9|  0  8  8   9  8   9   9   9  8  9   9   9   9   9   9   9
   10|  0  8  8  10  8  10  10  10  8  9  10  10  10  10  10  10
   11|  0  8  8  11  8  10  11  11  8  9  10  11  11  11  11  11
   12|  0  8  8  12  8  10  12  12  8  9  10  11  12  12  12  12
   13|  0  8  8  12  8  10  12  13  8  9  10  11  12  13  13  13
   14|  0  8  8  12  8  10  12  14  8  9  10  11  12  13  14  14
   15|  0  8  8  12  8  10  12  14  8  9  10  11  12  13  14  15
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010
• Rémy Sigrist, Colored representation of the table for n, k < 2^10

Crossrefs

Cf. A003983, A053644, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344838 (max), A344839 (absolute difference).

Programs

PARI

T(n, k, op=min, w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(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, 1) = A053644(n).