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%I #24 May 24 2022 17:52:10
%S 7,14,15,28,29,30,56,58,60,61,112,116,117,120,122,224,232,234,240,241,
%T 244,245,267,448,464,468,469,480,482,483,488,490,497,534,535,537,896,
%U 928,936,938,960,964,965,966,976,980,981,985,994,995,1068,1069,1070,1073
%N Numbers with 6 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)) = 6; A006667(a(n)) = 5.
%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="/A062056/b062056.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 7 is (7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 6 odd integers.
%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[1000], countOdd[Collatz[#]] == 6 &] (* _T. D. Noe_, Dec 03 2012 *)
%o (Haskell)
%o import Data.List (elemIndices)
%o a062056 n = a062056_list !! (n-1)
%o a062056_list = map (+ 1) $ elemIndices 6 a078719_list
%o -- _Reinhard Zumkeller_, Oct 08 2011
%Y Cf. A062052-A062060.
%Y Column k=6 of A354236.
%K nonn
%O 1,1
%A _David W. Wilson_
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