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A343042
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Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the factorial base.
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3
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0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 2, 8, 8, 2, 0, 0, 3, 6, 9, 6, 3, 0, 0, 6, 8, 8, 8, 8, 6, 0, 0, 7, 24, 9, 12, 9, 24, 7, 0, 0, 8, 26, 30, 14, 14, 30, 26, 8, 0, 0, 9, 30, 33, 24, 15, 24, 33, 30, 9, 0, 0, 8, 32, 32, 26, 30, 30, 26, 32, 32, 8, 0
(list;
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refs;
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history;
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OFFSET
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0,8
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COMMENTS
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To compute T(n, k):
- write the factorial base representations of n and of k on two lines, right aligned,
- to "multiply" two digits: take the smallest,
- to "add" two digits: take the largest,
- for example, for T(13, 14):
12 -> 2 0 1
14 -> x 2 1 0
-------
0 0 0
1 0 1
+ 2 0 1
-----------
2 1 1 1 0 -> 272 = T(13, 14)
See A343040 for the corresponding addition table.
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LINKS
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FORMULA
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T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, 0) = 0.
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EXAMPLE
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Array T(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12
---+---------------------------------------------------------
0| 0 0 0 0 0 0 0 0 0 0 0 0 0
1| 0 1 2 3 2 3 6 7 8 9 8 9 6
2| 0 2 6 8 6 8 24 26 30 32 30 32 24
3| 0 3 8 9 8 9 30 33 32 33 32 33 30
4| 0 2 6 8 12 14 24 26 30 32 36 38 48
5| 0 3 8 9 14 15 30 33 32 33 38 39 54
6| 0 6 24 30 24 30 120 126 144 150 144 150 120
7| 0 7 26 33 26 33 126 127 152 153 152 153 126
8| 0 8 30 32 30 32 144 152 150 152 150 152 144
9| 0 9 32 33 32 33 150 153 152 153 152 153 150
10| 0 8 30 32 36 38 144 152 150 152 156 158 168
11| 0 9 32 33 38 39 150 153 152 153 158 159 174
12| 0 6 24 30 48 54 120 126 144 150 168 174 240
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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