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A223083 Trajectory of 64 under the map n-> A006369(n).

%I A223083 #16 Mar 01 2019 09:01:16
%S A223083 64,85,113,151,201,134,179,239,319,425,567,378,252,168,112,149,199,
%T A223083 265,353,471,314,419,559,745,993,662,883,1177,1569,1046,1395,930,620,
%U A223083 827,1103,1471,1961,2615,3487,4649,6199,8265,5510,7347,4898,6531,4354,5805
%N A223083 Trajectory of 64 under the map n-> A006369(n).
%C A223083 It is conjectured that this trajectory does not close on itself.
%H A223083 T. D. Noe, <a href="/A223083/b223083.txt">Table of n, a(n) for n = 1..10000</a>
%H A223083 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 A223083 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 A223083 t1:=[64];
%p A223083 for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
%p A223083 t1;
%t A223083 t = {64}; 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 A223083 SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n - 1)/3, _, (4n + 1)/3]}, {64}, 60] // Flatten (* _Jean-François Alcover_, Mar 01 2019 *)
%Y A223083 Cf. A006369, A006368, A182205.
%Y A223083 Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.
%K A223083 nonn
%O A223083 1,1
%A A223083 _N. J. A. Sloane_, Mar 22 2013