OFFSET
1,1
COMMENTS
If a term k is even, then k/2 is also in the sequence.
For each odd term k among the first 15 terms, 2*k is also a term. Does the sequence include any odd terms k for which 2*k is not also in the sequence?
If it exists, a(16) > 1.5*10^11. - Giovanni Resta, May 04 2018
LINKS
EXAMPLE
The Collatz trajectory of 31 begins 31 -> 94 -> 47 -> 142 -> 71 -> 214 -> 107 -> 322 -> 161 -> 484 -> 242 -> 121 -> 364 -> 182 -> 91 -> 274 -> 137 -> 412 -> 206 -> 103 -> 310 -> 155 -> 466 -> ... which contains 310 and 155, both of which are multiples of 31, so 31 is in the sequence.
Other than its initial value, the trajectory of 62 is the same as that of 31, so it also includes 310, which is a multiple of 62, so 62 is in the sequence.
The trajectory of 671 includes 29524 = 671 * 11 * 2^2, so the sequence includes 671, 671*2 = 1342, and 671*4 = 2684.
MATHEMATICA
traj[1]:={1};
traj[n_]:=traj[n]=If[EvenQ[n]&&n>0, {n}~Join~traj[n/2], {n}~Join~traj[3*n+1]];
fQ[n_]:=Select[traj[n], IntegerQ[#/n]&&#/n>1&, 1]!={};
Select[Range[20000], fQ[#]&] (* Ivan N. Ianakiev, Apr 30 2018 *)
PROG
(Magma) a:=[]; for k in [2..40000] do t:=k; while t gt 1 do if IsEven(t) then t:=t div 2; else t:=3*t+1; end if; if IsDivisibleBy(t, k) then a[#a+1]:=k; break; end if; end while; end for; a; // Jon E. Schoenfield, Apr 30 2018
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jon E. Schoenfield, Apr 28 2018
STATUS
approved