A213672 Final term in Collatz trajectory of n that did not appear in previous trajectories.

1, 2, 4, 0, 0, 6, 20, 0, 14, 0, 0, 12, 0, 0, 80, 0, 0, 18, 44, 0, 32, 0, 0, 24, 38, 0, 92, 0, 0, 30, 0, 0, 50, 0, 0, 36, 56, 0, 152, 0, 0, 42, 74, 0, 68, 0, 0, 48, 0, 0, 116, 0, 0, 54, 188, 0, 86, 0, 0, 60, 0, 0, 728, 0, 0, 66, 0, 0, 104, 0, 0, 72, 110, 0, 128, 0

Offset: 1

Author

Jayanta Basu, Mar 03 2013

Keywords

• nonn

Comments

This can be considered as the step down value, as beyond this point the trajectory of n reduces to a lower trajectory. When n is impure we define a(n)=0; see also A177729.

Examples

			a(7)=20 because after 20 trajectory of 7 becomes identical with trajectory of 3.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A177729, A222118.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; prev = {}; Table[c = Collatz[n]; If[Complement[c, prev] == {}, 0, i = 1; While[MemberQ[prev, c[[-i]]], i++]; prev = Union[prev, c]; c[[-i]]], {n, 100}] (* T. D. Noe, Mar 03 2013 *)