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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. 3

%I #4 Jun 07 2015 18:02:51

%S 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 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 10,8,10,12,10,12,8,10,12,10,12,6,8,10,8

%N 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 a(n) = number of edges from 0 to n in the tree at A258235.

%H Clark Kimberling, <a href="/A258236/b258236.txt">Table of n, a(n) for n = 0..10000</a>

%e 29->75->28->10->3->7->2->0, so that a(29) = 7.

%t r = GoldenRatio^2; w = Table[Floor[r*n], {n, 1, 1000}];

%t f[x_] := If[MemberQ[w, x], Floor[x/r], Floor[r*x]];

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

%t Table[-1+ Length[g[n]], {n, 0, 100}]

%Y Cf. A258235, A258212, A001950.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 05 2015

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Last modified August 29 06:09 EDT 2024. Contains 375510 sequences. (Running on oeis4.)