A223086 - OEIS

%I #15 Mar 01 2019 08:47:15

%S 64,96,144,216,324,486,729,547,410,615,461,346,519,389,292,438,657,

%T 493,370,555,416,624,936,1404,2106,3159,2369,1777,1333,1000,1500,2250,

%U 3375,2531,1898,2847,2135,1601,1201,901,676,1014,1521,1141,856,1284,1926,2889

%N Trajectory of 64 under the map n-> A006368(n).

%C It is conjectured that this trajectory does not close on itself.

%H T. D. Noe, <a href="/A223086/b223086.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:=[64];

%p for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:

%p t1;

%t t = {64}; 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]]}, {64}, 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