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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A334290 Array read by upward antidiagonals: T(n,k) (n > 0, k > 0) = nim-division of n by k.

Original entry on oeis.org

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
Offset: 1

Views

Author

Rémy Sigrist, Jun 13 2020

Keywords

Comments

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

Examples

			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)

Links

Crossrefs

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

Programs

  • PARI
    See Links section.

Formula

T(n, k) = A051776(n, A051917(k)).
T(n, 1) = n.
T(1, n) = A051917(k).
T(n, n) = 1.

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

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Jun 13 2020

Keywords

Comments

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

Examples

			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)

Links

Crossrefs

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

Formula

T(n, k) = A051775(n, A051917(k)).
T(n, 1) = n.
T(1, n) = A051917(k).
T(n, n) = 1.
Previous Showing 11-12 of 12 results.

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