cp's OEIS Frontend

A235499 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(3).

%I A235499 #27 Dec 14 2021 14:59:23
%S A235499 0,1,2,3,9,10,11,12,13,19,20,21,22,23,29,30,31,32,33,39,40,41,42,43,
%T A235499 49,50,51,52,53,59,60,61,62,63,69,70,71,72,73,79,80,81,82,83,89,90,91,
%U A235499 92,93,99,100,101,102,103,109,110,111,112,113,119,120,121,122,123,129
%N A235499 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(3).
%H A235499 Vincenzo Librandi, <a href="/A235499/b235499.txt">Table of n, a(n) for n = 0..1000</a>
%H A235499 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A235499 G.f.: (x^5+6*x^4+x^3+x^2+x)/(x^6-x^5-x+1). - _Alois P. Heinz_, Feb 07 2014
%t A235499 CoefficientList[Series[(x^5 + 6 x^4 + x^3 + x^2 + x)/(x^6 - x^5 - x + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Feb 08 2014 *)
%t A235499 nxt[n_]:=If[Mod[n,10]==3,FromDigits[Join[Most[IntegerDigits[n]],{9}]], n+ 1]; NestList[nxt,0,70] (* or *) LinearRecurrence[{1,0,0,0,1,-1},{0,1,2,3,9,10},70] (* _Harvey P. Dale_, Oct 02 2016 *)
%Y A235499 Cf. A235498, A237341, A237342, A237343, A237344, A237345, A237346.
%K A235499 nonn,base,easy
%O A235499 0,3
%A A235499 _Vincenzo Librandi_, Feb 06 2014
%E A235499 Definition by _N. J. A. Sloane_, Feb 07 2014