%I #17 Mar 01 2019 08:47:08
%S 80,120,180,270,405,304,456,684,1026,1539,1154,1731,1298,1947,1460,
%T 2190,3285,2464,3696,5544,8316,12474,18711,14033,10525,7894,11841,
%U 8881,6661,4996,7494,11241,8431,6323,4742,7113,5335,4001,3001,2251,1688,2532,3798,5697
%N Trajectory of 80 under the map n-> A006368(n).
%C It is conjectured that this trajectory does not close on itself.
%H T. D. Noe, <a href="/A223087/b223087.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:=n-> if n mod 2 = 0 then 3*n/2 elif n mod 4 = 1 then (3*n+1)/4 else (3*n-1)/4; fi;
%p t1:=[80];
%p for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
%p t1;
%t t = {80}; While[n = t[[-1]]; s = If[EvenQ[n], 3*n/2, Round[3*n/4]]; Length[t] < 100 && ! MemberQ[t, s], AppendTo[t, s]]; t (* _T. D. Noe_, Mar 22 2013 *)
%t SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {80}, 100] // Flatten (* _Jean-François Alcover_, Mar 01 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