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%I #25 May 24 2022 17:52:58
%S 25,49,50,51,98,99,100,101,102,196,197,198,200,202,204,205,217,392,
%T 394,396,397,400,404,405,408,410,433,434,435,441,475,784,788,789,792,
%U 794,800,808,810,816,820,821,833,857,866,867,868,869,870,875,882,883,950,951,953
%N Numbers with 8 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)) = 8; A006667(a(n)) = 7.
%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="/A062058/b062058.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 25 is (25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 8 odd integers.
%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[1000], countOdd[Collatz[#]] == 8 &] (* _T. D. Noe_, Dec 03 2012 *)
%o (Haskell)
%o import Data.List (elemIndices)
%o a062058 n = a062058_list !! (n-1)
%o a062058_list = map (+ 1) $ elemIndices 8 a078719_list
%o -- _Reinhard Zumkeller_, Oct 08 2011
%Y Cf. A062052-A062060.
%Y Column k=8 of A354236.
%K nonn
%O 1,1
%A _David W. Wilson_
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