A258248 - OEIS

%I #5 Jun 11 2015 16:02:49

%S 0,2,1,3,5,3,5,7,2,4,6,4,6,8,6,8,4,6,8,6,8,10,8,10,12,3,5,7,5,7,9,7,9,

%T 5,7,9,7,9,11,9,11,13,7,9,11,9,11,13,5,7,7,9,11,9,11,13,7,9,11,9,11,

%U 13,11,13,15,9,11,11,13,15,13,15,17,4,6,8,6,8

%N Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A022842 (the Beatty sequence for sqrt(8)) and x -> [r*x] otherwise, where r = sqrt(8) and [ ] = floor.

%C a(n) = number of edges from 0 to n in the tree at A258247.

%H Clark Kimberling, <a href="/A258248/b258248.txt">Table of n, a(n) for n = 0..10000</a>

%e 13->36->12->33->11->3->8->2->0, so that a(12) = 8.

%t r = Sqrt[8]; 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. A022842, A258247, A258212.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 08 2015