%I #24 Sep 08 2022 08:46:03
%S 1,5,25,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,
%T 625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,
%U 125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625,125,625
%N a(n) = 5^n mod 1000.
%C Period = 2.
%C Also, continued fraction expansion of 1 + (150625 - 3*sqrt(43405))/755998. - _Bruno Berselli_, Sep 03 2012
%H Antti Karttunen, <a href="/A216125/b216125.txt">Table of n, a(n) for n = 0..1001</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F G.f.: (1 + 5*x + 24*x^2 + 120*x^3 + 600*x^4)/((1 - x)*(1 + x)). - _Bruno Berselli_, Sep 03 2012
%t PowerMod[5, Range[0, 100], 1000] (* _Vincenzo Librandi_, Aug 16 2016 *)
%o (PARI) for(i=0, 100, print(5^i%1000" "))
%o (Magma) [Modexp(5, n, 1000): n in [0..110]]; // _Vincenzo Librandi_, Aug 16 2016
%K nonn,easy
%O 0,2
%A _V. Raman_, Sep 01 2012
%E a(0) = 1 prepended and offset changed by _Vincenzo Librandi_, Aug 16 2016
%E Edited by _Bruno Berselli_, Aug 16 2016
%E More terms from _Antti Karttunen_, Sep 14 2017