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A343046
Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the primorial base.
3
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, 30, 9, 12, 9, 30, 7, 0, 0, 8, 32, 36, 14, 14, 36, 32, 8, 0, 0, 9, 36, 39, 30, 15, 30, 39, 36, 9, 0, 0, 8, 38, 38, 32, 36, 36, 32, 38, 38, 8, 0
OFFSET
0,8
COMMENTS
To compute T(n, k):
- write the primorial 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(9, 10):
9 -> 1 1 1
10 -> x 1 2 0
-------
0 0 0
1 1 1
+ 1 1 1
-----------
1 1 1 1 0 -> 248 = T(9, 10)
See A343044 for the corresponding addition table.
FORMULA
T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, 0) = 0.
T(n, 1) = A328841(n).
T(n, n) = A343047(n).
EXAMPLE
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 -> A328841
2| 0 2 6 8 6 8 30 32 36 38 36 38 30
3| 0 3 8 9 8 9 36 39 38 39 38 39 36
4| 0 2 6 8 12 14 30 32 36 38 42 44 60
5| 0 3 8 9 14 15 36 39 38 39 44 45 66
6| 0 6 30 36 30 36 210 216 240 246 240 246 210
7| 0 7 32 39 32 39 216 217 248 249 248 249 216
8| 0 8 36 38 36 38 240 248 246 248 246 248 240
9| 0 9 38 39 38 39 246 249 248 249 248 249 246
10| 0 8 36 38 42 44 240 248 246 248 252 254 270
11| 0 9 38 39 44 45 246 249 248 249 254 255 276
12| 0 6 30 36 60 66 210 216 240 246 270 276 420
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base,tabl
AUTHOR
Rémy Sigrist, Apr 05 2021
STATUS
approved