A372810 a(n) is the smallest number whose Collatz trajectory contains n, if trajectories do not terminate at 1 but continue to cycle through 1, 4, 2, 1, 4, 2, 1, ... .

1, 1, 3, 1, 3, 6, 7, 3, 9, 3, 7, 12, 7, 9, 15, 3, 7, 18, 19, 7, 21, 7, 15, 24, 25, 7, 27, 9, 19, 30, 27, 21, 33, 7, 15, 36, 37, 25, 39, 7, 27, 42, 43, 19, 45, 15, 27, 48, 43, 33, 51, 7, 15, 54, 55, 37, 57, 19, 39, 60, 27, 27, 63, 21, 43, 66, 39, 45, 69, 15, 27

Offset: 1

Author

Ethan E. Wood, May 13 2024

Keywords

• nonn

Comments

a(n) = A070167(n) for n >= 5.

a(n) = n if 3 divides n.

Examples

			For n=8,
  the trajectory of 1 is 1,  4, 2,  1, 4, ... (8 does not appear), and
  the trajectory of 2 is 2,  1, 4,  2, 1, ... (8 does not appear), but
  the trajectory of 3 is 3, 10, 5, 16, 8, ... (8 does appear),
so a(8) = 3.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, E16.

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A070167 (sequence resulting if trajectories terminate at 1).

Extensions

Edited by Jon E. Schoenfield, May 13 2024