A344839 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = abs(n * 2^max(0, w(k)-w(n)) - k * 2^max(0, w(n)-w(k))) (where w = A070939).

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

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(n, n) = 0.

T(n, 0) = n.

T(n, 1) = A053645(n) for any n > 0.

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  0  0  1  0  1  2  3  0  1   2   3   4   5   6   7
    2|   2  0  0  1  0  1  2  3  0  1   2   3   4   5   6   7
    3|   3  1  1  0  2  1  0  1  4  3   2   1   0   1   2   3
    4|   4  0  0  2  0  1  2  3  0  1   2   3   4   5   6   7
    5|   5  1  1  1  1  0  1  2  2  1   0   1   2   3   4   5
    6|   6  2  2  0  2  1  0  1  4  3   2   1   0   1   2   3
    7|   7  3  3  1  3  2  1  0  6  5   4   3   2   1   0   1
    8|   8  0  0  4  0  2  4  6  0  1   2   3   4   5   6   7
    9|   9  1  1  3  1  1  3  5  1  0   1   2   3   4   5   6
   10|  10  2  2  2  2  0  2  4  2  1   0   1   2   3   4   5
   11|  11  3  3  1  3  1  1  3  3  2   1   0   1   2   3   4
   12|  12  4  4  0  4  2  0  2  4  3   2   1   0   1   2   3
   13|  13  5  5  1  5  3  1  1  5  4   3   2   1   0   1   2
   14|  14  6  6  2  6  4  2  0  6  5   4   3   2   1   0   1
   15|  15  7  7  3  7  5  3  1  7  6   5   4   3   2   1   0

Prog

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

Crossrefs

Cf. A049581, A053645, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344837 (min), A344838 (max).

Sequence in context: A128064 A144217 A187881 * A344836 A323474 A132814

Adjacent sequences: A344836 A344837 A344838 * A344840 A344841 A344842

Keyword

nonn,base,tabl

Author

Rémy Sigrist, May 29 2021

Status

approved