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A334290 Array read by upward antidiagonals: T(n,k) (n > 0, k > 0) = nim-division of n by k. 2
1, 2, 3, 3, 1, 2, 4, 2, 3, 15, 5, 12, 1, 5, 12, 6, 15, 8, 10, 4, 9, 7, 13, 10, 1, 8, 14, 11, 8, 14, 11, 14, 13, 7, 13, 10, 9, 4, 9, 4, 1, 15, 6, 15, 6, 10, 7, 12, 11, 9, 6, 7, 5, 11, 8, 11, 5, 14, 2, 5, 1, 12, 3, 13, 12, 7, 12, 6, 15, 13, 6, 8, 10, 9, 14, 4, 9, 5 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each row and each column is a permutation of the natural numbers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..5050

Rémy Sigrist, PARI program for A334290

Index entries for sequences related to Nim-multiplication

FORMULA

T(n, k) = A051776(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

  ---+------------------------------------------------------------

    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)

PROG

(PARI) See Links section.

CROSSREFS

Cf. A004468, A004474, A004477, A004480, A006015, A051775, A051776, A051917, A334291.

Sequence in context: A108132 A106589 A335490 * A294101 A051911 A106595

Adjacent sequences:  A334287 A334288 A334289 * A334291 A334292 A334293

KEYWORD

nonn,tabl

AUTHOR

Rémy Sigrist, Jun 13 2020

STATUS

approved

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Last modified September 18 07:21 EDT 2020. Contains 337166 sequences. (Running on oeis4.)