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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(4).
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%I #23 Jul 01 2023 14:07:37

%S 0,1,2,3,4,16,17,18,19,20,21,22,23,24,216,217,218,219,220,221,222,223,

%T 224,2216,2217,2218,2219,2220,2221,2222,2223,2224,22216,22217,22218,

%U 22219,22220,22221,22222,22223,22224,222216,222217,222218,222219,222220,222221

%N 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(4).

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

%F G.f.: (10*x^17 +20*x^16 +30*x^15 +40*x^14 -20*x^13 -10*x^12 +10*x^10 +20*x^9 +19*x^8 +18*x^7 +17*x^6 +16*x^5 +4*x^4 +3*x^3 +2*x^2 +x)/(10*x^18 -11*x^9 +1). - _Alois P. Heinz_, Feb 07 2014

%Y Cf. A235498, A235499, A237341 - A237346.

%K nonn,base,easy

%O 0,3

%A _Vincenzo Librandi_, Feb 06 2014

%E Definition by _N. J. A. Sloane_, Feb 07 2014