A336111 - OEIS

%I #19 Aug 25 2020 00:16:54

%S 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,

%T 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,

%U 7,4,5,1,1,1,1,1,1,0,1,4,9,6,2,0,0,4,4,0,2,0,0

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

%C Although all numbers appear to be present, 1 appears most often followed by 0.

%C 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.

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

%H Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" from Vardi</a>

%e \m   1  2  3  4  5  6  7  8  9 10 11 12 13  14  15  16 ...

%e n\

%e _1   0  1  1  1  1  1  1  1  1  1  1  1  1   1   1   1

%e _2   0  0  1  0  1  4  2  0  7  6  9  4  3   2   1   0

%e _3   0  1  0  3  2  3  6  3  0  7  9  3  1  13  12  11

%e _4   0  0  1  0  1  4  4  0  4  6  4  4  9   4   1   0

%e _5   0  1  2  1  0  5  3  5  2  5  1  5  5   3   5   5

%e _6   0  0  0  0  1  0  1  0  0  6  5  0  1   8   6   0

%e _7   0  1  1  3  3  1  0  7  7  3  2  7  6   7  13   7

%e _8   0  0  1  0  1  4  1  0  1  6  3  4  1   8   1   0

%e _9   0  1  0  1  4  3  1  1  0  9  5  9  1   1   9   9

%e 10   0  0  1  0  0  4  4  0  1  0  1  4  3   4  10   0

%e etc, .

%t (* first load all lines of Super Power Mod by Ilan Vardi from the hyper-link *)

%t Table[ SuperPowerMod[n - m + 1, 2^100, m], {n, 14}, {m, n, 1, -1}] // Flatten (* or *)

%t 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

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

%K nonn,tabl

%O 1,18

%A _Jinyuan Wang_ and _Robert G. Wilson v_, Apr 15 2020