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A258246 Number of steps from n to 0, where allowable steps are x -> [x/Pi] if x = is in A022844 (the Beatty sequence for Pi) and x -> [Pi*x] otherwise, where [ ] = floor.

%I A258246 #4 Jun 11 2015 10:36:21
%S A258246 0,2,4,1,3,5,3,5,7,5,7,9,2,4,6,4,6,8,6,8,10,4,6,8,10,6,8,10,8,10,12,6,
%T A258246 8,10,8,10,12,10,12,14,3,5,7,5,7,9,11,7,9,11,5,7,9,7,9,11,9,11,13,7,9,
%U A258246 11,9,11,13,11,13,15,17,5,7,9,7,9,11,9,11,13
%N A258246 Number of steps from n to 0, where allowable steps are x -> [x/Pi] if x = is in A022844 (the Beatty sequence for Pi) and x -> [Pi*x] otherwise, where [ ] = floor.
%C A258246 a(n) = number of edges from 0 to n in the tree at A258245.
%H A258246 Clark Kimberling, <a href="/A258246/b258246.txt">Table of n, a(n) for n = 0..10000</a>
%e A258246 8->25->7->21->6->1->3->0, so that a(8) = 7.
%t A258246 r = Pi; w = Table[Floor[r*n], {n, 1, 1000}];
%t A258246 f[x_] := If[MemberQ[w, x], Floor[x/r], Floor[r*x]];
%t A258246 g[x_] := Drop[FixedPointList[f, x], -1];
%t A258246 Table[-1+ Length[g[n]], {n, 0, 100}]
%Y A258246 Cf. A022844, A258245, A258212.
%K A258246 nonn,easy
%O A258246 0,2
%A A258246 _Clark Kimberling_, Jun 08 2015