A308149 Positive integers with Collatz trajectories that do not include the number 5.

1, 2, 4, 8, 16, 21, 32, 42, 64, 75, 84, 85, 113, 128, 150, 151, 168, 170, 201, 226, 227, 256, 267, 300, 301, 302, 336, 340, 341, 401, 402, 403, 423, 452, 453, 454, 475, 512, 534, 535, 537, 600, 602, 604, 605, 633, 635, 672, 680, 682, 713, 715, 802, 803, 804, 805, 806, 846, 847, 891, 904, 906, 908, 909, 950, 951, 953, 955

Offset: 1

Author

Nathan Bumber, May 14 2019

Keywords

• nonn
• easy

Comments

A consequence of the Collatz conjecture is that, after a(5), this would be equivalent to the list of positive integers with Collatz trajectories that include the number 32.

Examples

			21 is a term because its Collatz trajectory, given in A033481, does not include 5.
		

Links

• Anonymous, Archive of /sci/ - Conjecture.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A033481, A070165.

A000079 is a subsequence.

Programs

Mathematica

collatzTrajectory[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[1000], Not[MemberQ[collatzTrajectory[#], 5]] &] (* Alonso del Arte, May 25 2019 *)