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A354438
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Square array A(n, k), n, k >= 0, read by antidiagonals; the factorial base expansion of A(n, k) is obtained by adding componentwise and reducing modulo their radix the digits of the factorial base expansions of n and k.
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2
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0, 1, 1, 2, 0, 2, 3, 3, 3, 3, 4, 2, 4, 2, 4, 5, 5, 5, 5, 5, 5, 6, 4, 0, 4, 0, 4, 6, 7, 7, 1, 1, 1, 1, 7, 7, 8, 6, 8, 0, 2, 0, 8, 6, 8, 9, 9, 9, 9, 3, 3, 9, 9, 9, 9, 10, 8, 10, 8, 10, 2, 10, 8, 10, 8, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET
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0,4
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COMMENTS
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The nonnegative integers together with A form an abelian group; A225901 gives inverse elements.
Each row is a permutation of the nonnegative integers.
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LINKS
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FORMULA
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A(n, k) = A(k, n).
A(m, A(n, k)) = A(A(m, n), k).
A(n, 0) = n.
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EXAMPLE
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Square array A(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+----------------------------------------------------------------
0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1| 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14
2| 2 3 4 5 0 1 8 9 10 11 6 7 14 15 16 17
3| 3 2 5 4 1 0 9 8 11 10 7 6 15 14 17 16
4| 4 5 0 1 2 3 10 11 6 7 8 9 16 17 12 13
5| 5 4 1 0 3 2 11 10 7 6 9 8 17 16 13 12
6| 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
7| 7 6 9 8 11 10 13 12 15 14 17 16 19 18 21 20
8| 8 9 10 11 6 7 14 15 16 17 12 13 20 21 22 23
9| 9 8 11 10 7 6 15 14 17 16 13 12 21 20 23 22
10| 10 11 6 7 8 9 16 17 12 13 14 15 22 23 18 19
11| 11 10 7 6 9 8 17 16 13 12 15 14 23 22 19 18
12| 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3
13| 13 12 15 14 17 16 19 18 21 20 23 22 1 0 3 2
14| 14 15 16 17 12 13 20 21 22 23 18 19 2 3 4 5
15| 15 14 17 16 13 12 21 20 23 22 19 18 3 2 5 4
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PROG
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(PARI) A(n, k, s=i->i+1) = { my (v=0, f=1, r); for (i=1, oo, if (n==0 && k==0, return (v), r=s(i); v+=f*((n+k)%r); f*=r; n\=r; k\=r)) }
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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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