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A223088 Trajectory of 82 under the map n-> A006368(n).

%I A223088 #16 Mar 01 2019 08:46:56
%S A223088 82,123,92,138,207,155,116,174,261,196,294,441,331,248,372,558,837,
%T A223088 628,942,1413,1060,1590,2385,1789,1342,2013,1510,2265,1699,1274,1911,
%U A223088 1433,1075,806,1209,907,680,1020,1530,2295,1721,1291,968,1452,2178,3267,2450,3675
%N A223088 Trajectory of 82 under the map n-> A006368(n).
%C A223088 It is conjectured that this trajectory does not close on itself.
%H A223088 T. D. Noe, <a href="/A223088/b223088.txt">Table of n, a(n) for n = 1..10000</a>
%H A223088 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 A223088 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 A223088 t1:=[82];
%p A223088 for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
%p A223088 t1;
%t A223088 t = {82}; 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 A223088 SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {82}, 100] // Flatten (* _Jean-François Alcover_, Mar 01 2019 *)
%Y A223088 Cf. A006369, A006368, A182205.
%Y A223088 Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.
%K A223088 nonn
%O A223088 1,1
%A A223088 _N. J. A. Sloane_, Mar 22 2013