A237342 - OEIS

A237342

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(5).

%I #24 Jul 01 2023 14:06:04

%S 0,1,2,3,4,5,25,225,2225,22225,222225,2222225,22222225,222222225,

%T 2222222225,22222222225,222222222225,2222222222225,22222222222225,

%U 222222222222225,2222222222222225,22222222222222225,222222222222222225,2222222222222222225

%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(5).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11, -10).

%F G.f.: (10*x^6-9*x^5-9*x^4-9*x^3-9*x^2+x)/(10*x^2-11*x+1). - _Alois P. Heinz_, Feb 07 2014

%F a(n) = ( 25 + 2*10^(n-4) )/9 for n>4. [_Bruno Berselli_, Feb 08 2014]

%t Join[Range[0, 4], Table[(25 + 2 10^(n - 4))/9, {n, 5, 30}]] (* _Bruno Berselli_, Feb 08 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