A334291 Array read by upward antidiagonals: T(n,k) (n >= 0, k > 0) = nim-division of n by k.

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

Offset

0,4

Comments

This is the array A334290 with a leading row of 0's.

Links

Table of n, a(n) for n=0..76.

Index entries for sequences related to Nim-multiplication

Formula

T(n, k) = A051775(n, A051917(k)).

T(n, 1) = n.

T(1, n) = A051917(k).

T(n, n) = 1.

Example

The array begins:
  n\k|   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
    1|   1   3   2  15  12   9  11  10   6   8   7   5  14  13   4 --> A051917(n)
    2|   2   1   3   5   4  14  13  15  11  12   9  10   7   6   8
    3|   3   2   1  10   8   7   6   5  13   4  14  15   9  11  12
    4|   4  12   8   1  13  15   7   3  14  11  10   2   5   9   6
    5|   5  15  10  14   1   6  12   9   8   3  13   7  11   4   2
    6|   6  13  11   4   9   1  10  12   5   7   3   8   2  15  14
    7|   7  14   9  11   5   8   1   6   3  15   4  13  12   2  10
    8|   8   4  12   2   6   5   9   1   7  13  15   3  10  14  11
    9|   9   7  14  13  10  12   2  11   1   5   8   6   4   3  15
   10|  10   5  15   7   2  11   4  14  12   1   6   9  13   8   3
   11|  11   6  13   8  14   2  15   4  10   9   1  12   3   5   7
   12|  12   8   4   3  11  10  14   2   9   6   5   1  15   7  13
   13|  13  11   6  12   7   3   5   8  15  14   2   4   1  10   9
   14|  14   9   7   6  15   4   3  13   2  10  12  11   8   1   5
   15|  15  10   5   9   3  13   8   7   4   2  11  14   6  12   1
             |   |   |   |   |
             |   |   |   |   A004474(n)
             |   |   |   A004477(n)
             |   |   A004480(n)
             |   A006015(n)
             A004468(n)

Crossrefs

Cf. A004468, A004474, A004477, A004480, A006015, A051775, A051776, A051917, A334290.

Sequence in context: A089235 A347794 A317948 * A051910 A137998 A316590

Adjacent sequences: A334288 A334289 A334290 * A334292 A334293 A334294

Keyword

nonn,tabl

Author

Rémy Sigrist, Jun 13 2020

Status

approved