A344835 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) OR (k * 2^max(0, w(n)-w(k))) (where OR denotes the bitwise OR operator and w = A070939).

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 6, 6, 5, 6, 7, 8, 7, 6, 7, 4, 7, 6, 7, 8, 9, 8, 7, 6, 5, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 10, 9, 12, 7, 7, 7, 7, 12, 9, 10, 11, 12, 11, 10, 13, 8, 7, 6, 7, 8, 13, 10, 11, 12

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 apply the bitwise OR operator.

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   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    1|   1   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    2|   2   2   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    3|   3   3   3   3   6   7   6   7  12  13  14  15  12  13  14  15
    4|   4   4   4   6   4   5   6   7   8   9  10  11  12  13  14  15
    5|   5   5   5   7   5   5   7   7  10  11  10  11  14  15  14  15
    6|   6   6   6   6   6   7   6   7  12  13  14  15  12  13  14  15
    7|   7   7   7   7   7   7   7   7  14  15  14  15  14  15  14  15
    8|   8   8   8  12   8  10  12  14   8   9  10  11  12  13  14  15
    9|   9   9   9  13   9  11  13  15   9   9  11  11  13  13  15  15
   10|  10  10  10  14  10  10  14  14  10  11  10  11  14  15  14  15
   11|  11  11  11  15  11  11  15  15  11  11  11  11  15  15  15  15
   12|  12  12  12  12  12  14  12  14  12  13  14  15  12  13  14  15
   13|  13  13  13  13  13  15  13  15  13  13  15  15  13  13  15  15
   14|  14  14  14  14  14  14  14  14  14  15  14  15  14  15  14  15
   15|  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15  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. A003986, A070939.

Cf. A344834 (AND), A344836 (XOR), A344837 (min), A344838 (max), A344839 (absolute difference).

Programs

PARI

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

T(n, 1) = max(1, n).