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A229481 Final digit of 1^n + 2^n + ... + n^n.

%I A229481 #21 Jan 02 2024 00:00:34
%S A229481 0,1,5,6,4,5,1,4,2,5,5,6,0,1,5,0,8,3,9,0,6,1,5,6,0,5,1,4,8,5,5,6,6,1,
%T A229481 5,0,4,3,9,0,2,1,5,6,6,5,1,4,4,5,5,6,2,1,5,0,0,3,9,0,8,1,5,6,2,5,1,4,
%U A229481 0,5,5,6,8,1,5,0,6,3,9,0,4,1,5,6,8,5,1,4,6,5,5,6,4,1,5,0,2,3,9,0
%N A229481 Final digit of 1^n + 2^n + ... + n^n.
%C A229481 Cyclic with period 100.
%H A229481 Alois P. Heinz, <a href="/A229481/b229481.txt">Table of n, a(n) for n = 0..1000</a>
%H A229481 <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).
%F A229481 a(n) = a(n-100). - _Wesley Ivan Hurt_, Jan 02 2024
%p A229481 a:= proc(n) local l; l:=[seq(add(k&^i mod 10, k=1..i) mod 10, i=0..99)]:
%p A229481       proc(n) l[1+irem(n, 100)] end
%p A229481     end():
%p A229481 seq(a(n), n=0..200);  # _Alois P. Heinz_, Sep 26 2013
%t A229481 Table[Mod[Sum[PowerMod[i, n, 10], {i, 1, n}], 10], {n, 0, 133}]
%o A229481 (PARI) a(n)=n%=100;lift(sum(k=1,n,Mod(k,10)^n)) \\ _Charles R Greathouse IV_, Dec 13 2013
%Y A229481 Cf. A031971, A056849.
%K A229481 nonn,base,easy
%O A229481 0,3
%A A229481 _José María Grau Ribas_, Sep 24 2013