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%I #31 Nov 15 2023 12:22:57
%S 0,1,2,9,44,25,76,1,8,21,0,1,12,81,64,25,76,81,68,41,0,1,22,29,24,25,
%T 76,61,28,61,0,1,32,61,84,25,76,41,88,81,0,1,42,49,4,25,76,21,48,1,50,
%U 1,52,41,4,25,76,1,58,21,0,1,62,69,84,25,76,81,68,41,0,1
%N a(n) = n^a(n-1) mod 100; a(0) = 0.
%C a(n+100) = a(n).
%C 0 <= a(n) <= 94 for all integers n.
%C a(10*k) = 0.
%C a(n+1) = 1 and a(n+2) = n mod 100 iff a(n)=0.
%C Limit_{n->oo} (1/n)*Sum_{j=1..n} a(j) = 38.3.
%H Robert G. Wilson v, <a href="/A345414/b345414.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_100">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%e a(2) = 2^1 mod 100 = 2 mod 100 = 2;
%e a(3) = 3^2 mod 100 = 9 mod 100 = 9;
%e a(4) = 4^9 mod 100 = 262144 mod 100 = 44;
%e a(5) = 5^44 mod 100 = 5684341886080801486968994140625 mod 100 = 25.
%t a[n_] := Mod[n^a[n - 1], 100]; a[0] = 0; Array[a, 72, 0] (* _Robert G. Wilson v_, Nov 14 2023 *)
%K nonn,easy,less
%O 0,3
%A _Joseph Neeley_, Jun 18 2021
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