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%I #48 Dec 18 2023 17:25:39
%S 0,1,6,1,6,5,6,1,6,1,0,1,6,1,6,5,6,1,6,1,0,1,6,1,6,5,6,1,6,1,0,1,6,1,
%T 6,5,6,1,6,1,0,1,6,1,6,5,6,1,6,1,0,1,6,1,6,5,6,1,6,1,0,1,6,1,6,5,6,1,
%U 6,1,0,1,6,1,6,5,6,1,6,1,0,1,6,1,6,5,6,1,6,1,0,1,6,1,6,5,6,1,6,1,0
%N Final digit of n^4: a(n) = n^4 mod 10.
%C Decimal expansion of 538853870/3333333333. - _Alexander R. Povolotsky_, Mar 09 2013
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F a(n) = n^k mod 10; for k > 0 where k mod 4 = 0. - _Doug Bell_, Jun 15 2015
%F From _G. C. Greubel_, Apr 01 2016: (Start)
%F a(n) = a(n-10).
%F a(2*n) = 6*A011558(n).
%F G.f.: (x +6*x^2 +x^3 +6*x^4 +5*x^5 +6*x^6 +x^7 +6*x^8 +x^9)/(1 - x^10). (End)
%p A070514:=n->n^4 mod 10: seq(A070514(n), n=0..100); # _Wesley Ivan Hurt_, Apr 01 2016
%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 6, 1, 6, 5, 6, 1, 6, 1}, 100] (* _Vincenzo Librandi_, Jun 16 2015 *)
%t PowerMod[Range[0, 100], 4, 10] (* _G. C. Greubel_, Apr 01 2016 *)
%o (Sage) [power_mod(n,4,10)for n in range(0, 101)] # _Zerinvary Lajos_, Oct 30 2009
%o (Magma) [n^4 mod (10): n in [0..80]]; // _Vincenzo Librandi_, Jun 16 2015
%o (PARI) vector(100,n,n--;n^4%10) \\ _Derek Orr_, Jun 16 2015
%Y Cf. A010879, A008959, A008960. - _Doug Bell_, Jun 15 2015
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, May 13 2002
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