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A082984
Numbers k for which the 3x+1 problem takes at least k halving and tripling steps to reach 1.
4
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
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
KEYWORD
nonn,hard,more
AUTHOR
Hauke Worpel (hw1(AT)email.com), May 29 2003
STATUS
approved