A182205 - OEIS

%I #21 Mar 01 2019 08:46:30

%S 40,60,90,135,101,76,114,171,128,192,288,432,648,972,1458,2187,1640,

%T 2460,3690,5535,4151,3113,2335,1751,1313,985,739,554,831,623,467,350,

%U 525,394,591,443,332,498,747,560,840,1260,1890,2835,2126,3189,2392,3588,5382

%N Iterate the map in A006368 starting at 40.

%C Like for iterations with starting points 8 or 14, it is conjectured that also this trajectory never repeats.

%D D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998; see p. 16.

%H Reinhard Zumkeller, <a href="/A182205/b182205.txt">Table of n, a(n) for n = 0..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.

%F a(n+1) = A006368(a(n)), with a(0) = 40.

%t SubstitutionSystem[{n_ :> If[EvenQ[n], 3 n/2, Round[3 n/4]]}, {40}, 60] // Flatten (* _Jean-François Alcover_, Mar 01 2019 *)

%o (Haskell)

%o a182205 n = a182205_list !! n

%o a182205_list = iterate a006368 40

%Y Cf. A028393, A028395, A180853, A180864, A182205; A028398(6) = 40.

%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 0,1

%A _Reinhard Zumkeller_, Apr 18 2012