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

1,2

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A177729, A222118.

Sequence in context: A298368 A072069 A230423 * A309244 A378518 A004025

Adjacent sequences: A213669 A213670 A213671 * A213673 A213674 A213675

Keyword

nonn

Author

Jayanta Basu, Mar 03 2013

Status

approved