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Final digit of real part of (n+n*i)^n.
2

%I #19 Oct 21 2023 09:31:14

%S 1,0,6,6,0,0,4,6,4,0,8,6,8,0,0,6,2,0,2,0,6,0,6,6,0,0,4,6,4,0,8,6,8,0,

%T 0,6,2,0,2,0,6,0,6,6,0,0,4,6,4,0,8,6,8,0,0,6,2,0,2,0,6,0,6,6,0,0,4,6,

%U 4,0,8,6,8,0,0,6,2,0,2,0,6,0,6,6,0,0

%N Final digit of real part of (n+n*i)^n.

%C Starting from a(2) the sequence is periodic with period length 20. - _Giovanni Resta_, Feb 23 2014

%H Vincenzo Librandi, <a href="/A238291/b238291.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_20">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, 1).

%t re[n_, b_] := Mod[b + Re@PowerMod[(n + n I), n, b], b];

%t Table[re[n, 10], {n, 100}]

%Y Cf. A238292, A056849.

%K nonn,base

%O 1,3

%A _José María Grau Ribas_, Feb 22 2014