A336111 A non-symmetrical rectangular array read by antidiagonals: A(n,m) is the tower of powers of n modulo m.

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

Offset: 1

Author

Jinyuan Wang and Robert G. Wilson v, Apr 15 2020

Keywords

• nonn
• tabl

Comments

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.

Examples

			\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, .
		

References

• Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.

Links

• Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi

Crossrefs

Cf. A245970, A240162, A245971, A245972, A245973, A245974, A332055, A332054.

Programs

Mathematica

(* 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