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a(n) is the n-th decimal digit from the right in n^n.
1

%I #9 Jun 21 2022 19:54:42

%S 1,0,0,0,0,0,0,1,3,0,8,9,2,1,8,6,4,4,9,0,0,7,9,8,0,0,0,3,1,0,5,1,8,1,

%T 5,7,8,2,4,0,4,1,8,7,4,0,3,8,1,0,6,1,3,8,3,4,9,3,3,0,1,1,9,6,8,2,1,6,

%U 5,0,8,6,8,5,0,7,1,1,2,0,3,8,3,3,3,8,2,5,3,0,4,1,0,6,3,5,3,2,7,0

%N a(n) is the n-th decimal digit from the right in n^n.

%C If 2 <= n <= 7, n^n has fewer than n digits, so a(n) is taken to be 0.

%C a(n) = 0 if n is divisible by 10.

%H Robert Israel, <a href="/A281298/b281298.txt">Table of n, a(n) for n = 1..10000</a>

%e 8^8 = 16777216 so a(8) = 1.

%p seq(10^(1-m)*((m &^m mod 10^m) - (m &^ m mod 10^(m-1))), m=1..1000);

%o (Python)

%o def a(n): return pow(n, n, 10**n)//10**(n-1)

%o print([a(n) for n in range(1, 101)]) # _Michael S. Branicky_, Jun 21 2022

%Y Cf. A000312.

%K nonn,base

%O 1,9

%A _Robert Israel_, Jan 19 2017