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%I #14 May 24 2022 17:54:35
%S 39,78,79,153,156,157,158,305,306,307,312,314,315,316,317,610,611,612,
%T 613,614,624,628,629,630,631,632,634,647,683,687,1220,1221,1222,1224,
%U 1226,1228,1229,1241,1248,1256,1257,1258,1260,1261,1262,1264,1265,1268
%N Numbers with 12 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. The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.
%D J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
%H Harvey P. Dale, <a href="/A072122/b072122.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 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%e trajectory: 39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 has 12 odd numbers.
%t odd12Q[n_]:=Count[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&], _?OddQ]==12; Select[Range[1300],odd12Q] (* _Harvey P. Dale_, Oct 17 2011 *)
%Y Cf. A062052-A062060.
%Y Column k=12 of A354236.
%K easy,nonn
%O 1,1
%A _Jim Nastos_, Jun 19 2002
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