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Numbers with 5 odd integers in their Collatz (or 3x+1) trajectory.
8

%I #26 May 24 2022 17:51:41

%S 11,22,23,44,45,46,88,90,92,93,176,180,181,184,186,201,352,360,362,

%T 368,369,372,373,401,402,403,704,720,724,725,736,738,739,744,746,753,

%U 802,803,804,805,806,1408,1440,1448,1450,1472,1476,1477,1478,1488,1492,1493,1506

%N Numbers with 5 odd integers in their Collatz (or 3x+1) trajectory.

%C The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd.

%C The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.

%C A078719(a(n)) = 5; A006667(a(n)) = 4.

%D J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.

%H Reinhard Zumkeller, <a href="/A062055/b062055.txt">Table of n, a(n) for n = 1..1000</a>

%H J. Shallit and D. Wilson, <a href="http://www.cs.uwaterloo.ca/~shallit/Papers/wilson.ps">The "3x+1" Problem and Finite Automata</a>, Bulletin of the EATCS #46 (1992) pp. 182-185.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.

%e The Collatz trajectory of 11 is (11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 5 odd integers.

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[2000], countOdd[Collatz[#]] == 5 &] (* _T. D. Noe_, Dec 03 2012 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a062055 n = a062055_list !! (n-1)

%o a062055_list = map (+ 1) $ elemIndices 5 a078719_list

%o -- _Reinhard Zumkeller_, Oct 08 2011

%Y Cf. A062052-A062060.

%Y Column k=5 of A354236.

%K nonn

%O 1,1

%A _David W. Wilson_