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A336111
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A non-symmetrical rectangular array read by antidiagonals: A(n,m) is the tower of powers of n modulo m.
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1
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0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 3, 1, 1, 0, 1, 4, 2, 0, 2, 0, 0, 1, 2, 3, 1, 1, 0, 1, 0, 1, 0, 6, 4, 0, 0, 1, 0, 0, 1, 7, 3, 4, 5, 1, 3, 1, 1, 0, 1, 6, 0, 0, 3, 0, 3, 0, 0, 0, 0, 1, 9, 7, 4, 5, 1, 1, 1, 1, 1, 1, 0, 1, 4, 9, 6, 2, 0, 0, 4, 4, 0, 2, 0, 0
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OFFSET
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1,18
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COMMENTS
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Although all numbers appear to be present, 1 appears most often followed by 0.
Since the first column and main diagonal are equal to 0, all matrices whose upper left corner is on the main diagonal have as their determinant 0.
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REFERENCES
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Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
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LINKS
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EXAMPLE
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\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...
n\
_1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
_2 0 0 1 0 1 4 2 0 7 6 9 4 3 2 1 0
_3 0 1 0 3 2 3 6 3 0 7 9 3 1 13 12 11
_4 0 0 1 0 1 4 4 0 4 6 4 4 9 4 1 0
_5 0 1 2 1 0 5 3 5 2 5 1 5 5 3 5 5
_6 0 0 0 0 1 0 1 0 0 6 5 0 1 8 6 0
_7 0 1 1 3 3 1 0 7 7 3 2 7 6 7 13 7
_8 0 0 1 0 1 4 1 0 1 6 3 4 1 8 1 0
_9 0 1 0 1 4 3 1 1 0 9 5 9 1 1 9 9
10 0 0 1 0 0 4 4 0 1 0 1 4 3 4 10 0
etc, .
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MATHEMATICA
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(* first load all lines of Super Power Mod by Ilan Vardi from the hyper-link *)
Table[ SuperPowerMod[n - m + 1, 2^100, m], {n, 14}, {m, n, 1, -1}] // Flatten (* or *)
a[b_, 1] = 0; a[b_, n_] := PowerMod[b, If[OddQ@ b, a[b, EulerPhi[n]], EulerPhi[n] + a[b, EulerPhi[n]]], n]; Table[a[b - m + 1, m], {b, 14}, {m, b, 1, -1}] // Flatten
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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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