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

%I A334290 #26 Jun 15 2020 03:17:28
%S A334290 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,
%T A334290 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,
%U A334290 14,2,5,1,12,3,13,12,7,12,6,15,13,6,8,10,9,14,4,9,5
%N A334290 Array read by upward antidiagonals: T(n,k) (n > 0, k > 0) = nim-division of n by k.
%C A334290 Each row and each column is a permutation of the natural numbers.
%H A334290 Rémy Sigrist, <a href="/A334290/b334290.txt">Table of n, a(n) for n = 1..5050</a>
%H A334290 Rémy Sigrist, <a href="/A334290/a334290.gp.txt">PARI program for A334290</a>
%H A334290 <a href="/index/Ni#Nimmult">Index entries for sequences related to Nim-multiplication</a>
%F A334290 T(n, k) = A051776(n, A051917(k)).
%F A334290 T(n, 1) = n.
%F A334290 T(1, n) = A051917(k).
%F A334290 T(n, n) = 1.
%e A334290 The array begins:
%e A334290   n\k|   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
%e A334290   ---+------------------------------------------------------------
%e A334290     1|   1   3   2  15  12   9  11  10   6   8   7   5  14  13   4 --> A051917(n)
%e A334290     2|   2   1   3   5   4  14  13  15  11  12   9  10   7   6   8
%e A334290     3|   3   2   1  10   8   7   6   5  13   4  14  15   9  11  12
%e A334290     4|   4  12   8   1  13  15   7   3  14  11  10   2   5   9   6
%e A334290     5|   5  15  10  14   1   6  12   9   8   3  13   7  11   4   2
%e A334290     6|   6  13  11   4   9   1  10  12   5   7   3   8   2  15  14
%e A334290     7|   7  14   9  11   5   8   1   6   3  15   4  13  12   2  10
%e A334290     8|   8   4  12   2   6   5   9   1   7  13  15   3  10  14  11
%e A334290     9|   9   7  14  13  10  12   2  11   1   5   8   6   4   3  15
%e A334290    10|  10   5  15   7   2  11   4  14  12   1   6   9  13   8   3
%e A334290    11|  11   6  13   8  14   2  15   4  10   9   1  12   3   5   7
%e A334290    12|  12   8   4   3  11  10  14   2   9   6   5   1  15   7  13
%e A334290    13|  13  11   6  12   7   3   5   8  15  14   2   4   1  10   9
%e A334290    14|  14   9   7   6  15   4   3  13   2  10  12  11   8   1   5
%e A334290    15|  15  10   5   9   3  13   8   7   4   2  11  14   6  12   1
%e A334290              |   |   |   |   |
%e A334290              |   |   |   |   A004474(n)
%e A334290              |   |   |   A004477(n)
%e A334290              |   |   A004480(n)
%e A334290              |   A006015(n)
%e A334290              A004468(n)
%o A334290 (PARI) See Links section.
%Y A334290 Cf. A004468, A004474, A004477, A004480, A006015, A051775, A051776, A051917, A334291.
%K A334290 nonn,tabl
%O A334290 1,2
%A A334290 _Rémy Sigrist_, Jun 13 2020