A237415 - OEIS

%I #29 Mar 02 2024 14:20:21

%S 0,1,2,8,9,10,11,12,18,19,20,21,22,28,29,30,31,32,38,39,40,41,42,48,

%T 49,50,51,52,58,59,60,61,62,68,69,70,71,72,78,79,80,81,82,88,89,90,91,

%U 92,98,99,100,101,102,108,109,110,111,112,118,119,120,121,122,128

%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^3. This is k(2).

%C Nonnegative integers m such that floor(2*m^2/10) = 2*floor(m^2/10). [_Bruno Berselli_, Dec 08 2015]

%H Vincenzo Librandi, <a href="/A237415/b237415.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F G.f.: x*(1 + x + 6*x^2 + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)). [_Bruno Berselli_, Feb 08 2014]

%F a(n) = a(n-1)+a(n-5)-a(n-6). - _Vincenzo Librandi_, Feb 12 2014

%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 8, 9, 10}, 70] (* _Bruno Berselli_, Feb 08 2014 *)

%t CoefficientList[Series[x (1 + x + 6 x^2 + x^3 + x^4)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Feb 12 2014 *)

%t NestList[If[Mod[#,10]==2,FromDigits[Join[Most[IntegerDigits[#]],{8}]], #+ 1]&,0,100] (* _Harvey P. Dale_, Feb 21 2016 *)

%o (Magma) I:=[0,1,2,8,9,10]; [n le 6 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..80]]; // _Vincenzo Librandi_, Feb 12 2014

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

%K nonn,base,easy

%O 0,3

%A _Vincenzo Librandi_, Feb 07 2014

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