A355245 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 least 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, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 2, 1, 0, 0, 4, 2, 2, 4, 0, 0, 1, 4, 3, 4, 1, 0, 0, 2, 2, 4, 4, 2, 2, 0, 0, 1, 2, 5, 4, 5, 2, 1, 0, 0, 8, 2, 6, 4, 4, 6, 2, 8, 0, 0, 1, 8, 3, 4, 5, 4, 3, 8, 1, 0, 0, 2, 2, 8, 4, 6, 6, 4, 8, 2, 2, 0, 0, 1, 2, 9, 8, 5, 6, 5, 8, 9, 2, 1, 0

Offset

0,8

Comments

Leading 0's are taken into account.

Links

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

Formula

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

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

A(n, n) = n.

A(n, 0) = 0.

A(n, 1) = A006519(n) for any n > 0.

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

A(m, A355246(n, k)) = A355246(A(m, n), A(m, k)).

A355246(m, A(n, k)) = A(A355246(m, n), A355246(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  0  0   0  0   0   0   0  0   0   0   0   0   0   0   0
    1|  0  1  2   1  4   1   2   1  8   1   2   1   4   1   2   1
    2|  0  2  2   2  4   2   2   2  8   2   2   2   4   2   2   2
    3|  0  1  2   3  4   5   6   3  8   9  10   3  12   5   6   3
    4|  0  4  4   4  4   4   4   4  8   4   4   4   4   4   4   4
    5|  0  1  2   5  4   5   6   5  8   9  10   5  12   5   6   5
    6|  0  2  2   6  4   6   6   6  8  10  10   6  12   6   6   6
    7|  0  1  2   3  4   5   6   7  8   9  10  11  12  13  14   7
    8|  0  8  8   8  8   8   8   8  8   8   8   8   8   8   8   8
    9|  0  1  2   9  4   9  10   9  8   9  10   9  12   9  10   9
   10|  0  2  2  10  4  10  10  10  8  10  10  10  12  10  10  10
.
For n = 876 and k = 425:
- the corresponding binary expansions and pairings of 0's are as follows (stars indicate least 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
                 * * * *     *   *
             -----------------------------
       428   ... 0 0 0 0 1 1 0 1 0 1 1 0 0
- so A(876, 425) = 428.

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 (max(zn, zk)==w, w++, v+=b); n\=2; k\=2; b*=2); v }

Crossrefs

See A355246 for a similar sequence.

Cf. A006519.

Sequence in context: A263754 A328800 A328802 * A103822 A225927 A029392

Adjacent sequences: A355242 A355243 A355244 * A355246 A355247 A355248

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Jun 25 2022

Status

approved