A082984 Numbers k for which the 3x+1 problem takes at least k halving and tripling steps to reach 1.

1, 2, 3, 5, 6, 7, 9, 11, 14, 15, 18, 19, 27, 31, 41, 47, 54, 55, 62, 63, 71, 73, 82, 83, 91, 94, 95, 97, 108, 109, 110

Offset: 1

Author

Hauke Worpel (hw1(AT)email.com), May 29 2003

Keywords

• nonn
• hard
• more

Comments

This sequence is almost certainly full; there are no more terms below 100000.

An exhaustive search revealed no further results up to 10^9. - Gonzalo Ciruelos, Aug 02 2013

If we do not count the initial number, then 1 and 2 do not appear in this sequence. It appears that no number k has a Collatz iteration requiring more than 5*k iterations. - T. D. Noe, Feb 21 2014

Examples

			3 is in the list because it takes A006577(3) = 7 steps to reach 1 (3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1).
		

Links

• Gonzalo Ciruelos, Python script to generate the sequence.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006577, A006666, A008908.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[1000], Length[Collatz[#]] >= # &] (* T. D. Noe, Feb 21 2014 *)