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A341458
Unique square array T(n, k) read by antidiagonals, n, k > 0, such that A000069(T(n, k)) = A341288(A000069(n), A000069(k)).
4
1, 2, 2, 3, 1, 3, 4, 5, 5, 4, 5, 6, 1, 6, 5, 6, 3, 7, 7, 3, 6, 7, 4, 2, 1, 2, 4, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 7, 4, 2, 1, 2, 4, 7, 9, 10, 17, 6, 3, 7, 7, 3, 6, 17, 10, 11, 18, 33, 5, 6, 1, 6, 5, 33, 18, 11, 12, 22, 39, 57, 4, 5, 5, 4, 57, 39, 22, 12
OFFSET
1,2
COMMENTS
The positive integers equipped with T form a group.
Every row (and column) is a self-inverse permutation of the positive integers.
FORMULA
T(n, k) = T(k, n).
T(n, 1) = n.
T(n, n) = 1.
EXAMPLE
Array T(n, k) begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
---+--------------------------------------------------------------------------
1| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2| 2 1 5 6 3 4 8 7 17 18 22 21 20 19 23 24
3| 3 5 1 7 2 8 4 6 33 39 35 37 36 38 34 40
4| 4 6 7 1 8 2 3 5 57 63 62 60 61 59 58 64
5| 5 3 2 8 1 7 6 4 65 71 70 68 69 67 66 72
6| 6 4 8 2 7 1 5 3 89 95 91 93 92 94 90 96
7| 7 8 4 3 6 5 1 2 105 106 110 109 108 107 111 112
8| 8 7 6 5 4 3 2 1 113 114 115 116 117 118 119 120
9| 9 17 33 57 65 89 105 113 1 25 41 49 73 81 97 121
10| 10 18 39 63 71 95 106 114 25 1 56 48 88 80 121 97
11| 11 22 35 62 70 91 110 115 41 56 1 32 104 121 80 81
12| 12 21 37 60 68 93 109 116 49 48 32 1 121 104 88 73
13| 13 20 36 61 69 92 108 117 73 88 104 121 1 32 48 49
14| 14 19 38 59 67 94 107 118 81 80 121 104 32 1 56 41
15| 15 23 34 58 66 90 111 119 97 121 80 88 48 56 1 25
16| 16 24 40 64 72 96 112 120 121 97 81 73 49 41 25 1
PROG
(PARI) See Links section.
CROSSREFS
See A341487 and A341489 for the second and third rows, respectively.
Sequence in context: A289236 A280172 A337942 * A089913 A257522 A059897
KEYWORD
nonn,tabl,base
AUTHOR
Rémy Sigrist, Feb 12 2021
STATUS
approved