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A258240 Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A001952 (the Beatty sequence for 2 + sqrt(2)) and x -> [r*x] otherwise, where [ ] = floor and r = 2 + sqrt(2). 3

%I

%S 0,2,4,1,3,5,3,5,7,9,5,7,9,2,4,6,8,4,6,8,6,8,10,4,6,8,10,6,8,10,8,10,

%T 12,14,10,12,14,6,8,10,8,10,12,14,10,12,14,3,5,7,9,5,7,9,7,9,11,13,9,

%U 11,13,5,7,9,7,9,11,13,9,11,13,7,9,11,13,9,11

%N Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A001952 (the Beatty sequence for 2 + sqrt(2)) and x -> [r*x] otherwise, where [ ] = floor and r = 2 + sqrt(2).

%C a(n) = number of edges from 0 to n in the tree at A258239.

%H Clark Kimberling, <a href="/A258240/b258240.txt">Table of n, a(n) for n = 0..10000</a>

%e 8->27->7->23->6->1->3->0, so that a(8) = 7.

%t r = 2+Sqrt[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. A258239, A258212, A001952.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 05 2015

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)