A258215 - OEIS

%I #4 Jun 07 2015 18:02:31

%S 0,1,3,2,4,6,3,5,5,7,9,4,6,8,6,8,8,10,12,5,7,7,9,11,7,9,11,9,11,11,13,

%T 15,6,8,10,8,10,10,12,14,8,10,10,12,14,10,12,14,12,14,14,16,18,7,9,9,

%U 11,13,9,11,13,11,13,13,15,17,9,11,13,11,13,13,15

%N Number of steps from n to 0, where allowable steps are x -> [x/r] if x is in lower Wythoff sequence (A000201) and x -> [r*x] otherwise, where [ ] = floor and r = (1+sqrt(5))/2 = golden ratio.

%C a(n) = number of edges from 0 to n in the tree at A258212.

%H Clark Kimberling, <a href="/A258215/b258215.txt">Table of n, a(n) for n = 0..10000</a>

%e 35->21->12->7->11->6->3->1->0, so that a(35) = 8.

%t r = GoldenRatio; 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. A258212, A000201.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 05 2015