cp's OEIS Frontend

A258215 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.

%I A258215 #4 Jun 07 2015 18:02:31
%S A258215 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 A258215 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 A258215 11,13,9,11,13,11,13,13,15,17,9,11,13,11,13,13,15
%N A258215 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 A258215 a(n) = number of edges from 0 to n in the tree at A258212.
%H A258215 Clark Kimberling, <a href="/A258215/b258215.txt">Table of n, a(n) for n = 0..10000</a>
%e A258215 35->21->12->7->11->6->3->1->0, so that a(35) = 8.
%t A258215 r = GoldenRatio; w = Table[Floor[r*n], {n, 1, 1000}];
%t A258215 f[x_] := If[MemberQ[w, x], Floor[x/r], Floor[r*x]];
%t A258215 g[x_] := Drop[FixedPointList[f, x], -1];
%t A258215 Table[-1+ Length[g[n]], {n, 0, 100}]
%Y A258215 Cf. A258212, A000201.
%K A258215 nonn,easy
%O A258215 0,3
%A A258215 _Clark Kimberling_, Jun 05 2015