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%I #59 May 24 2022 17:51:22
%S 17,34,35,68,69,70,75,136,138,140,141,150,151,272,276,277,280,282,300,
%T 301,302,544,552,554,560,564,565,600,602,604,605,1088,1104,1108,1109,
%U 1120,1128,1130,1137,1200,1204,1205,1208,1210,2176,2208,2216,2218,2240
%N Numbers with 4 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)) = 4; A006667(a(n)) = 3.
%C Numbers m such that (s0 - 4s1)/2m = 1 where s0 is the sum of the even elements and s1 the sum of the odd elements in the Collatz trajectory of m. - _Michel Lagneau_, Aug 13 2018
%C If m is in the sequence then so is 2*m, so one would only have to check odd numbers. - _David A. Corneth_, Aug 13 2018
%D J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
%H David A. Corneth, <a href="/A062054/b062054.txt">Table of n, a(n) for n = 1..15549</a> (first 750 terms from Reinhard Zumkeller, terms < 10^15)
%H J. R. Goodwin, <a href="http://www.info.uaic.ro/bin/Annals/Article?v=XIII">Results on the Collatz Conjecture</a>, Sci. Ann. Comput. Sci. 13 (2003) pp. 1-16.
%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>.
%F The twelve formulas giving this sequence are listed in Corollary 3.3 in J. R. Goodwin with the following caveats: the value x cannot equal zero in formulas (3.16) and (3.20), one must multiply the formulas by all powers of 2 (2^1, 2^2, ...) to get the evens. - _Jeffrey R. Goodwin_, Oct 26 2011
%e The Collatz trajectory of 17 is (17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 4 odd integers. - _Jeffrey R. Goodwin_, Oct 26 2011
%t col4Q[n_]:=Module[{c=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#!=1&]}, Count[c,_?OddQ]==4]; Select[Range[2500],col4Q] (* _Harvey P. Dale_, Mar 21 2011 *)
%o (Haskell)
%o import Data.List (elemIndices)
%o a062054 n = a062054_list !! (n-1)
%o a062054_list = map (+ 1) $ elemIndices 4 a078719_list
%o -- _Reinhard Zumkeller_, Oct 08 2011
%Y Cf. A000079, A006370, A062052, A062053, A062055, A062056, A062057, A062058, A062059, A062060, A092893, A198587.
%Y Column k=4 of A354236.
%K nonn,easy
%O 1,1
%A _David W. Wilson_
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