A223085 Trajectory of 82 under the map n-> A006369(n).

82, 109, 145, 193, 257, 343, 457, 609, 406, 541, 721, 961, 1281, 854, 1139, 1519, 2025, 1350, 900, 600, 400, 533, 711, 474, 316, 421, 561, 374, 499, 665, 887, 1183, 1577, 2103, 1402, 1869, 1246, 1661, 2215, 2953, 3937, 5249, 6999, 4666, 6221, 8295, 5530, 7373

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:=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;
t1:=[82];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

Mathematica

t = {82}; 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 *)
SubstitutionSystem[{n_ :> Switch[Mod[n, 3], 0, 2n/3, 1, (4n - 1)/3, , (4n + 1)/3]}, {82}, 60] // Flatten (* _Jean-François Alcover, Mar 01 2019 *)
NestList[If[Divisible[#,3],(2#)/3,Floor[(4#)/3+1/2]]&,82,50] (* Harvey P. Dale, Sep 22 2019 *)