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a(n) = 6^n mod 1000.
1

%I #25 Sep 08 2022 08:46:03

%S 1,6,36,216,296,776,656,936,616,696,176,56,336,16,96,576,456,736,416,

%T 496,976,856,136,816,896,376,256,536,216,296,776,656,936,616,696,176,

%U 56,336,16,96,576,456,736,416,496,976,856,136,816,896,376,256,536,216,296,776

%N a(n) = 6^n mod 1000.

%C Terms 1, 6 and 36 occur only once. Period length = 25.

%H Vincenzo Librandi, <a href="/A216127/b216127.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%t PowerMod[6, Range[0, 100], 1000] (* _Vincenzo Librandi_, Aug 16 2016 *)

%t PadRight[{1,6,36},120,{376,256,536,216,296,776,656,936,616,696,176,56,336,16,96,576,456,736,416,496,976,856,136,816,896}] (* _Harvey P. Dale_, Jan 24 2022 *)

%o (PARI) for(i=0, 100, print(6^i%1000" "))

%o (Magma) [Modexp(6, n, 1000): n in [0..110]]; // _Vincenzo Librandi_, Aug 16 2016

%Y Cf. A001311.

%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