%I #4 Jun 07 2015 18:03:50

%S 0,1,3,2,4,4,3,5,5,7,5,7,4,6,8,6,8,8,10,6,8,10,5,7,7,9,11,7,9,9,11,9,

%T 11,13,7,9,9,11,11,6,8,8,10,8,10,10,12,14,8,10,10,10,12,12,14,10,12,

%U 12,14,16,8,10,10,12,10,12,14,12,14,7,9,9,9,11,11

%N Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A022838 (the Beatty sequence for sqrt(3)) and x -> [r*x] otherwise, where [ ] = floor and r = sqrt(3).

%C a(n) = number of edges from 0 to n in the tree at A258241.

%H Clark Kimberling, <a href="/A258242/b258242.txt">Table of n, a(n) for n = 0..10000</a>

%e 16->27->15->8->4->6->3->1->0, so that a(16) = 8.

%t r = Sqrt[3]; w = Table[Floor[r*n], {n, 1, 1000}];

%t f[x_] := If[MemberQ[w, x], Floor[x/r], Floor[r*x]];

%t g[x_] := Drop[FixedPointList[f, x], -1];

%t Table[-1+ Length[g[n]], {n, 0, 100}]

%Y Cf. A022838, A258241, A258212.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 07 2015