A355246 Square array A(n, k), n, k >= 0, read by antidiagonals; for any m > 0, the position of the m-th rightmost 0 in the binary expansion of A(n, k) is the greatest of the positions of the m-th rightmost 0 in the binary expansions of n and k (the least significant bit having position 0).

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

Offset

0,4

Comments

Leading 0's are taken into account.

Links

Table of n, a(n) for n=0..90.

Formula

A(n, k) = A(k, n).

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

A(n, n) = n.

A(n, n) = 0.

A(n, k) < 2^m for any n < 2^m and k < 2^m.

A(m, A355245(n, k)) = A355245(A(m, n), A(m, k)).

A355245(m, A(n, k)) = A(A355245(m, n), A355245(m, k)).

Example

Array A(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   1  3   1  5  5  7   1  9   9  11   9  13  13  15
    2|   2  1   2  3   2  5  6  7   2  9  10  11  10  13  14  15
    3|   3  3   3  3   3  3  3  7   3  3   3  11   3  11  11  15
    4|   4  1   2  3   4  5  6  7   4  9  10  11  12  13  14  15
    5|   5  5   5  3   5  5  5  7   5  5   5  11   5  13  13  15
    6|   6  5   6  3   6  5  6  7   6  5   6  11   6  13  14  15
    7|   7  7   7  7   7  7  7  7   7  7   7   7   7   7   7  15
    8|   8  1   2  3   4  5  6  7   8  9  10  11  12  13  14  15
    9|   9  9   9  3   9  5  5  7   9  9   9  11   9  13  13  15
   10|  10  9  10  3  10  5  6  7  10  9  10  11  10  13  14  15
.
For n = 876 and k = 425:
- the corresponding binary expansions and pairings of 0's are as follows (stars indicate greatest positions of 0's):
                 * * *     *     *
       876   ... 0 0 0 1 1 0 1 1 0 1 1 0 0
                  \ \ \     \    |    / /
       425   ... 0 0 0 0 1 1 0 1 0 1 0 0 1
                                 *   * *
             -----------------------------
       873   ... 0 0 0 1 1 0 1 1 0 1 0 0 1
- so A(876, 425) = 873.

Prog

(PARI) A(n, k) = { my (v=0, zn=0, zk=0, w=1, b=1); while (n || k, if (n%2==0, zn++); if (k%2==0, zk++); if (min(zn, zk)==w, w++, v+=b); n\=2; k\=2; b*=2); v }

Crossrefs

See A355245 for a similar sequence.

Sequence in context: A159335 A109004 A103823 * A136642 A080382 A349203

Adjacent sequences: A355243 A355244 A355245 * A355247 A355248 A355249

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Jun 25 2022

Status

approved