A217729 Trajectory of 40 under the map n-> A006369(n).

40, 53, 71, 95, 127, 169, 225, 150, 100, 133, 177, 118, 157, 209, 279, 186, 124, 165, 110, 147, 98, 131, 175, 233, 311, 415, 553, 737, 983, 1311, 874, 1165, 1553, 2071, 2761, 3681, 2454, 1636, 2181, 1454, 1939, 2585, 3447, 2298, 1532, 2043, 1362, 908, 1211, 1615

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:=[40];
for n from 1 to 100 do t1:=[op(t1),f(t1[nops(t1)])]; od:
t1;

Mathematica

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 *)
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 *)