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%I #18 Sep 22 2019 15:18:07
%S 82,109,145,193,257,343,457,609,406,541,721,961,1281,854,1139,1519,
%T 2025,1350,900,600,400,533,711,474,316,421,561,374,499,665,887,1183,
%U 1577,2103,1402,1869,1246,1661,2215,2953,3937,5249,6999,4666,6221,8295,5530,7373
%N Trajectory of 82 under the map n-> A006369(n).
%C It is conjectured that this trajectory does not close on itself.
%H T. D. Noe, <a href="/A223085/b223085.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 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 t1:=[82];
%p for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
%p t1;
%t t = {82}; 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 SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n - 1)/3, _, (4n + 1)/3]}, {82}, 60] // Flatten (* _Jean-François Alcover_, Mar 01 2019 *)
%t NestList[If[Divisible[#,3],(2#)/3,Floor[(4#)/3+1/2]]&,82,50] (* _Harvey P. Dale_, Sep 22 2019 *)
%Y Cf. A006369, A006368, A182205.
%Y Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Mar 22 2013
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