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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)