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%I #30 Jul 16 2021 01:40:55
%S 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,
%T 94,95,97,108,109,110
%N Numbers k for which the 3x+1 problem takes at least k halving and tripling steps to reach 1.
%C This sequence is almost certainly full; there are no more terms below 100000.
%C An exhaustive search revealed no further results up to 10^9. - _Gonzalo Ciruelos_, Aug 02 2013
%C 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
%H Gonzalo Ciruelos, <a href="/A082984/a082984.py.txt">Python script to generate the sequence.</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e 3 is in the list because it takes A006577(3) = 7 steps to reach 1 (3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1).
%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[1000], Length[Collatz[#]] >= # &] (* _T. D. Noe_, Feb 21 2014 *)
%Y Cf. A006577, A006666, A008908.
%K nonn,hard,more
%O 1,2
%A Hauke Worpel (hw1(AT)email.com), May 29 2003
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