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A257702 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).

%I A257702 #4 May 06 2015 09:49:26
%S A257702 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 A257702 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 A257702 16,10,14,8,10,10,12,10,14,12,18,14,16,18,20,5,9
%N A257702 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 A257702 Clark Kimberling, <a href="/A257702/b257702.txt">Table of n, a(n) for n = 1..10000</a>
%e A257702 5->11->24->10->4->1->2->0, total of 7 steps, so that a(5) = 7.
%t A257702 r = Sqrt[5]; f[x_] := If[OddQ[x], Floor[r *x], Floor[x/r]]
%t A257702 g[x_] := Drop[FixedPointList[f, x], -1];
%t A257702 Table[-1 + Length[g[n]], {n, 1, 200}]
%Y A257702 Cf. A257698-A257701, A257703-A257706.
%K A257702 nonn,easy
%O A257702 1,1
%A A257702 _Clark Kimberling_, May 04 2015