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A223084 Trajectory of 80 under the map n-> A006369(n).

%I A223084 #16 Mar 01 2019 09:25:01
%S A223084 80,107,143,191,255,170,227,303,202,269,359,479,639,426,284,379,505,
%T A223084 673,897,598,797,1063,1417,1889,2519,3359,4479,2986,3981,2654,3539,
%U A223084 4719,3146,4195,5593,7457,9943,13257,8838,5892,3928,5237,6983,9311,12415,16553,22071
%N A223084 Trajectory of 80 under the map n-> A006369(n).
%C A223084 It is conjectured that this trajectory does not close on itself.
%H A223084 T. D. Noe, <a href="/A223084/b223084.txt">Table of n, a(n) for n = 1..10000</a>
%H A223084 J. H. Conway, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.03.192">On unsettleable arithmetical problems</a>, Amer. Math. Monthly, 120 (2013), 192-198.
%p A223084 f:=proc(N) if N mod 3 = 0 then 2*(N/3); elif N mod 3 = 2 then 4*((N+1)/3)-1; else 4*((N+2)/3)-3; fi; end;
%p A223084 t1:=[80];
%p A223084 for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
%p A223084 t1;
%t A223084 t = {80}; While[n = t[[-1]]; s = Switch[Mod[n, 3], 0, 2*n/3, 1, (4*n - 1)/3, 2, (4*n + 1)/3]; Length[t] < 100 && ! MemberQ[t, s], AppendTo[t, s]]; t (* _T. D. Noe_, Mar 22 2013 *)
%t A223084 SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n - 1)/3, _, (4n + 1)/3]}, {80}, 60] // Flatten (* _Jean-François Alcover_, Mar 01 2019 *)
%Y A223084 Cf. A006369, A006368, A182205.
%Y A223084 Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.
%K A223084 nonn
%O A223084 1,1
%A A223084 _N. J. A. Sloane_, Mar 22 2013