cp's OEIS Frontend

A258236 Number of steps from n to 0, where allowable steps are x -> [x/r] if x is in upper Wythoff sequence (A001950) and x -> [r*x] otherwise, where [ ] = floor and r = (3+sqrt(5))/2.

%I A258236 #4 Jun 07 2015 18:02:51
%S A258236 0,2,1,3,5,3,5,2,4,6,4,6,8,6,8,4,6,8,6,8,3,5,7,5,7,9,7,9,5,7,9,7,9,11,
%T A258236 9,11,7,9,11,9,11,5,7,9,7,9,11,9,11,7,9,11,9,11,4,6,8,6,8,10,8,10,6,8,
%U A258236 10,8,10,12,10,12,8,10,12,10,12,6,8,10,8
%N A258236 Number of steps from n to 0, where allowable steps are x -> [x/r] if x is in upper Wythoff sequence (A001950) and x -> [r*x] otherwise, where [ ] = floor and r = (3+sqrt(5))/2.
%C A258236 a(n) = number of edges from 0 to n in the tree at A258235.
%H A258236 Clark Kimberling, <a href="/A258236/b258236.txt">Table of n, a(n) for n = 0..10000</a>
%e A258236 29->75->28->10->3->7->2->0, so that a(29) = 7.
%t A258236 r = GoldenRatio^2; w = Table[Floor[r*n], {n, 1, 1000}];
%t A258236 f[x_] := If[MemberQ[w, x], Floor[x/r], Floor[r*x]];
%t A258236 g[x_] := Drop[FixedPointList[f, x], -1];
%t A258236 Table[-1+ Length[g[n]], {n, 0, 100}]
%Y A258236 Cf. A258235, A258212, A001950.
%K A258236 nonn,easy
%O A258236 0,2
%A A258236 _Clark Kimberling_, Jun 05 2015