A344838 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = max(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where 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, 6, 4, 6, 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, 6, 6, 7, 12, 9, 10, 11, 12, 11, 10, 12, 8, 7, 6, 7, 8, 12, 10, 11, 12

Offset

0,4

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 greatest value.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10010

Rémy Sigrist, Colored representation of the table for n, k < 2^10

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).

Example

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   6   6   7  12  12  12  12  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   6   5   5   6   7  10  10  10  11  12  13  14  15
    6|   6   6   6   6   6   6   6   7  12  12  12  12  12  13  14  15
    7|   7   7   7   7   7   7   7   7  14  14  14  14  14  14  14  15
    8|   8   8   8  12   8  10  12  14   8   9  10  11  12  13  14  15
    9|   9   9   9  12   9  10  12  14   9   9  10  11  12  13  14  15
   10|  10  10  10  12  10  10  12  14  10  10  10  11  12  13  14  15
   11|  11  11  11  12  11  11  12  14  11  11  11  11  12  13  14  15
   12|  12  12  12  12  12  12  12  14  12  12  12  12  12  13  14  15
   13|  13  13  13  13  13  13  13  14  13  13  13  13  13  13  14  15
   14|  14  14  14  14  14  14  14  14  14  14  14  14  14  14  14  15
   15|  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15

Prog

(PARI) T(n, k, op=max, w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

Crossrefs

Cf. A003984, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344837 (min), A344839 (absolute difference).

Sequence in context: A231205 A003984 A087061 * A344835 A082860 A342859

Adjacent sequences: A344835 A344836 A344837 * A344839 A344840 A344841

Keyword

nonn,base,tabl

Author

Rémy Sigrist, May 29 2021

Status

approved