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

1,2

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

Links

Table of n, a(n) for n=1..31.

Gonzalo Ciruelos, Python script to generate the sequence.

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

Example

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

Mathematica

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

Crossrefs

Cf. A006577, A006666, A008908.

Sequence in context: A358221 A026453 A026455 * A085717 A253083 A108130

Adjacent sequences: A082981 A082982 A082983 * A082985 A082986 A082987

Keyword

nonn,hard,more

Author

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

Status

approved