A237344 - OEIS

%I #24 Jul 01 2023 14:09:40

%S 0,1,2,3,4,5,6,7,49,50,51,52,53,54,55,56,57,549,550,551,552,553,554,

%T 555,556,557,5549,5550,5551,5552,5553,5554,5555,5556,5557,55549,55550,

%U 55551,55552,55553,55554,55555,55556,55557,555549,555550,555551,555552

%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(7).

%H Vincenzo Librandi, <a href="/A237344/b237344.txt">Table of n, a(n) for n = 0..1000</a>

%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 -10*x^15 +10*x^13 +20*x^12 +30*x^11 +40*x^10 +50*x^9 +49*x^8 +7*x^7 +6*x^6 +5*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

%t CoefficientList[Series[(10 x^17 - 20 x^16 - 10 x^15 + 10 x^13 + 20 x^12 + 30 x^11 + 40 x^10 + 50 x^9 + 49 x^8 + 7 x^7 + 6 x^6 + 5 x^5 + 4 x^4 + 3 x^3 + 2 x^2 + x)/(10 x^18 -11 x^9 + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 24 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