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A088153 a(n) is the value of the n-th digit in the decimal representation of n^n.

%I A088153 #10 Feb 16 2025 08:32:51
%S A088153 1,0,0,0,0,0,0,0,0,0,1,2,8,0,1,7,4,2,6,1,6,7,7,9,6,7,2,3,5,2,9,3,9,7,
%T A088153 1,9,7,7,4,9,6,2,2,8,1,5,4,3,0,7,5,4,7,5,9,1,2,5,3,5,6,9,4,0,4,1,2,4,
%U A088153 6,5,9,9,0,1,4,9,1,6,7,1,6,7,7,0,6,6,5,9,0,0,1,7,0,6,3,7,5,2,6,2,0,8
%N A088153 a(n) is the value of the n-th digit in the decimal representation of n^n.
%C A088153 a(n) = d(n) with n^n = Sum_{0<=d(k)<10, k>=0} d(k)*10^k.
%H A088153 Robert Israel, <a href="/A088153/b088153.txt">Table of n, a(n) for n = 0..10000</a>
%H A088153 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Decimal.html">Decimal</a>
%F A088153 a(n) = floor(n^n / 10^n) mod 10.
%e A088153 For n=16, 16^16 = 18446744073709551616, a(16)=4.
%e A088153 a(0)=1, a(k)=0 for 0 < k < 10 and a(10)=1.
%p A088153 f:= proc(n) local x, L;
%p A088153    x:= n &^ n mod 10^(n+1);
%p A088153    floor(x/10^n)
%p A088153 end proc:
%p A088153 f(0):= 1:
%p A088153 map(f, [$0..101]); # _Robert Israel_, Dec 02 2022
%Y A088153 Cf. A000312, A088150, A088151, A088152, A088154, A088155, A088156, A088157.
%K A088153 nonn,base
%O A088153 0,12
%A A088153 _Reinhard Zumkeller_, Sep 20 2003