A217729 - OEIS

%I #19 Mar 01 2019 09:01:05

%S 40,53,71,95,127,169,225,150,100,133,177,118,157,209,279,186,124,165,

%T 110,147,98,131,175,233,311,415,553,737,983,1311,874,1165,1553,2071,

%U 2761,3681,2454,1636,2181,1454,1939,2585,3447,2298,1532,2043,1362,908,1211,1615

%N Trajectory of 40 under the map n-> A006369(n).

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

%H T. D. Noe, <a href="/A217729/b217729.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:=[40];

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

%p t1;

%t t = {40}; 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]}, {40}, 60] // 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