

A082984


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


3



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
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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 n has a Collatz iteration requiring more than 5*n 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.


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.
Sequence in context: A135607 A026453 A026455 * A085717 A253083 A108130
Adjacent sequences: A082981 A082982 A082983 * A082985 A082986 A082987


KEYWORD

nonn


AUTHOR

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


STATUS

approved



