A050016 - OEIS

A050016

a(n) = floor(a(n-1)/2) if this is positive and not yet in the sequence, otherwise a(n) = 9*a(n-1).

%I #12 Oct 05 2019 11:32:13

%S 1,9,4,2,18,162,81,40,20,10,5,45,22,11,99,49,24,12,6,3,27,13,117,58,

%T 29,14,7,63,31,15,135,67,33,16,8,72,36,324,2916,1458,729,364,182,91,

%U 819,409,204,102,51,25,225,112,56,28,252,126,1134

%N a(n) = floor(a(n-1)/2) if this is positive and not yet in the sequence, otherwise a(n) = 9*a(n-1).

%H Ivan Neretin, <a href="/A050016/b050016.txt">Table of n, a(n) for n = 1..10000</a>

%t Rest@Nest[Append[#, If[FreeQ[#, r = Quotient[#[[-1]], 2]], r, 9 #[[-1]]]] &, {0, 1}, 56] (* _Ivan Neretin_, Jul 31 2016 *)

%o (PARI) first(n)=my(v=vector(n), t); v[1]=1; for(i=2, n, t=v[i-1]\2; if(t<2, v[i]=9*v[i-1]; next); for(j=1, i-1, if(v[j]==t, v[i]=9*v[i-1]; next(2))); v[i]=t); v \\ _Charles R Greathouse IV_, Jul 31 2016

%Y Cf. A050000 and references therein.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_