A258238 - OEIS

A258238

Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A001951 (the Beatty sequence for sqrt(2)) and x -> [r*x] otherwise, where [ ] = floor and r = sqrt(2).

%I #4 Jun 07 2015 18:03:09

%S 0,1,2,4,3,5,7,4,6,8,10,5,7,9,9,11,6,8,8,10,12,10,12,14,7,9,9,11,11,

%T 13,15,11,13,15,17,8,10,12,10,12,14,12,14,16,18,12,14,16,16,18,9,11,

%U 11,13,15,11,13,15,17,13,15,17,17,19,21,13,15,17,19,17

%N Number of steps from n to 0, where allowable steps are x -> [x/r] if x = is in A001951 (the Beatty sequence for sqrt(2)) and x -> [r*x] otherwise, where [ ] = floor and r = sqrt(2).

%C a(n) = number of edges from 0 to n in the tree at A258237.

%H Clark Kimberling, <a href="/A258238/b258238.txt">Table of n, a(n) for n = 0..10000</a>

%e 36->25->17->24->16->11->7->4->2->1->0, so that a(36) = 10.

%t r = 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. A258237, A258212, A001951.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 05 2015