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Number of steps from n to 0 using this algorithm: x -> floor(r*x) if x is odd, and x -> floor(x/r) if x is even, where r = sqrt(5).
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%I #4 May 06 2015 09:49:26

%S 2,1,3,3,7,2,12,4,6,4,6,8,12,3,11,13,15,5,7,5,7,7,11,5,9,7,9,9,11,13,

%T 17,4,10,12,14,14,16,14,18,16,24,6,8,8,10,6,10,8,16,8,10,12,14,6,8,10,

%U 16,10,14,8,10,10,12,10,14,12,18,14,16,18,20,5,9

%N Number of steps from n to 0 using this algorithm: x -> floor(r*x) if x is odd, and x -> floor(x/r) if x is even, where r = sqrt(5).

%H Clark Kimberling, <a href="/A257702/b257702.txt">Table of n, a(n) for n = 1..10000</a>

%e 5->11->24->10->4->1->2->0, total of 7 steps, so that a(5) = 7.

%t r = Sqrt[5]; f[x_] := If[OddQ[x], Floor[r *x], Floor[x/r]]

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

%t Table[-1 + Length[g[n]], {n, 1, 200}]

%Y Cf. A257698-A257701, A257703-A257706.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, May 04 2015