A344834 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) AND (k * 2^max(0, w(n)-w(k))) (where AND denotes the bitwise AND operator and 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, 4, 4, 4, 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, 4, 4, 4, 8, 8, 8, 0, 0, 8, 8, 8, 8, 5, 6, 5, 8, 8, 8, 8, 0

Offset

0,8

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 AND operator.

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) = A053644(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  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   4   6   6  8  8   8   8  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   4  4   5   4   5  8  8  10  10   8   8  10  10
    6|  0  4  4   6  4   4   6   6  8  8   8   8  12  12  12  12
    7|  0  4  4   6  4   5   6   7  8  8  10  10  12  12  14  14
    8|  0  8  8   8  8   8   8   8  8  8   8   8   8   8   8   8
    9|  0  8  8   8  8   8   8   8  8  9   8   9   8   9   8   9
   10|  0  8  8   8  8  10   8  10  8  8  10  10   8   8  10  10
   11|  0  8  8   8  8  10   8  10  8  9  10  11   8   9  10  11
   12|  0  8  8  12  8   8  12  12  8  8   8   8  12  12  12  12
   13|  0  8  8  12  8   8  12  12  8  9   8   9  12  13  12  13
   14|  0  8  8  12  8  10  12  14  8  8  10  10  12  12  14  14
   15|  0  8  8  12  8  10  12  14  8  9  10  11  12  13  14  15

Prog

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

Crossrefs

Cf. A004198, A053644, A070939.

Cf. A344835 (OR), A344836 (XOR), A344837 (min), A344838 (max), A344839 (absolute difference).

Sequence in context: A015818 A225869 A039972 * A344837 A031124 A063695

Adjacent sequences: A344831 A344832 A344833 * A344835 A344836 A344837

Keyword

nonn,base,tabl

Author

Rémy Sigrist, May 29 2021

Status

approved