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%I #10 May 06 2015 09:45:42
%S 1,3,2,6,3,5,7,9,4,8,6,8,10,12,5,7,9,11,7,11,9,11,13,15,6,10,8,10,10,
%T 14,8,10,12,14,10,14,12,14,16,18,7,9,11,13,9,13,11,13,15,17,9,13,11,
%U 13,13,17,11,13,15,17,13,17,15,17,19,21,8,12,10
%N Algorithm: x->[rx] if x even, x->[rx-x] if x odd, where r = (1+sqrt(5))/2, []=floor; a(n) is the number of steps from x=n to 0.
%H Clark Kimberling, <a href="/A182649/b182649.txt">Table of n, a(n) for n = 1..1000</a>
%e 8->12->19->11->6->9->5->3->1->0; 9 steps, so that a(8) = 9.
%t r = GoldenRatio; f[x_] := If[OddQ[x], Floor[x/r], Floor[r*x]];
%t h[x_] := -1 + Length[Drop[FixedPointList[f, x], -1]];
%t Table[h[n], {n, 1, 100}] (* _Clark Kimberling_, May 04 2015 *)
%Y Cf. A182650, A182651, A182652.
%K nonn
%O 1,2
%A _Clark Kimberling_, Nov 26 2010
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