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Base 5 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,0,2.
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%I #10 Jun 26 2022 05:31:33

%S 1,8,40,202,1011,5058,25290,126452,632261,3161308,15806540,79032702,

%T 395163511,1975817558,9879087790,49395438952,246977194761,

%U 1234885973808,6174429869040,30872149345202,154360746726011,771803733630058

%N Base 5 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,0,2.

%H Harvey P. Dale, <a href="/A037703/b037703.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,0,1,-5).

%F G.f.: ( x*(1+3*x+2*x^3) ) / ( (x-1)*(5*x-1)*(1+x)*(x^2+1) ). - _R. J. Mathar_, Oct 13 2015

%F a(n) = 5*a(n-1) + a(n-4) - 5*a(n-5). - _Wesley Ivan Hurt_, Jun 26 2022

%t nn=30;With[{c=PadRight[{},nn,{1,3,0,2}]},Table[FromDigits[Take[c,n],5],{n,nn}]] (* _Harvey P. Dale_, Feb 16 2013 *)

%K nonn,base

%O 1,2

%A _Clark Kimberling_