A223087 Trajectory of 80 under the map n-> A006368(n).

80, 120, 180, 270, 405, 304, 456, 684, 1026, 1539, 1154, 1731, 1298, 1947, 1460, 2190, 3285, 2464, 3696, 5544, 8316, 12474, 18711, 14033, 10525, 7894, 11841, 8881, 6661, 4996, 7494, 11241, 8431, 6323, 4742, 7113, 5335, 4001, 3001, 2251, 1688, 2532, 3798, 5697

Offset: 1

Author

N. J. A. Sloane, Mar 22 2013

Keywords

• nonn

Comments

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• J. H. Conway, On unsettleable arithmetical problems, Amer. Math. Monthly, 120 (2013), 192-198.

Crossrefs

Cf. A006369, A006368, A182205.

Trajectories under A006368 and A006369: A180853, A217218, A185590, A180864, A028393, A028394, A094328, A094329, A028396, A028395, A217729, A182205, A223083-A223088, A185589, A185590.

Programs

Maple

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;
t1:=[80];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

Mathematica

t = {80}; 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 *)
SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {80}, 100] // Flatten (* Jean-François Alcover, Mar 01 2019 *)