OFFSET
1,1
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 22 2013
STATUS
approved