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A180864 Trajectory of 13 under map n->A006368(n).

%I A180864 #25 Mar 01 2019 08:46:46
%S A180864 13,10,15,11,8,12,18,27,20,30,45,34,51,38,57,43,32,48,72,108,162,243,
%T A180864 182,273,205,154,231,173,130,195,146,219,164,246,369,277,208,312,468,
%U A180864 702,1053,790,1185,889,667,500,750,1125,844,1266,1899,1424,2136,3204,4806,7209,5407,4055,3041,2281,1711,1283,962
%N A180864 Trajectory of 13 under map n->A006368(n).
%C A180864 Merges with the trajectory of 8 after four steps - see A028393.
%C A180864 It is a famous unsolved problem to show that this trajectory is unbounded.
%D A180864 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 A180864 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.
%H A180864 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A180864 a(n+1) = A006368(a(n)).
%t A180864 b[n_] := If[EvenQ[n], 3n/2, Floor[(3n+2)/4]];
%t A180864 a[0] = 13; a[n_] := a[n] = b[a[n-1]];
%t A180864 Table[a[n], {n, 0, 62}] (* _Jean-François Alcover_, Aug 01 2018 *)
%t A180864 SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {13}, 62] // Flatten (* _Jean-François Alcover_, Mar 01 2019 *)
%o A180864 (Haskell)
%o A180864 a180864 n = a180864_list !! n
%o A180864 a180864_list = iterate a006368 13  -- _Reinhard Zumkeller_, Apr 18 2012
%Y A180864 Cf. A006368, A028393, A028395, A028397.
%Y A180864 Cf. A180853, A182205.
%K A180864 nonn
%O A180864 0,1
%A A180864 _N. J. A. Sloane_, Jan 22 2011