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Start at n and iterate the map in A006368; a(n) is the smallest number in the trajectory.
6

%I #22 Aug 28 2016 18:23:38

%S 0,1,2,2,4,4,4,4,8,4,8,8,12,8,14,8,16,8,18,14,20,16,14,8,24,14,14,20,

%T 14,14,30,8,32,14,32,14,36,14,32,14,40,8,14,32,44,32,46,14,48,14,50,

%U 32,50,40,46,8,56,32,14,44,60,46,44,14,64,14,44,50,8,50,44,40,72,8,44,56

%N Start at n and iterate the map in A006368; a(n) is the smallest number in the trajectory.

%H T. D. Noe, <a href="/A028397/b028397.txt">Table of n, a(n) for n = 0..1000</a>

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

%e Sample iteration: 7->5->4->6->9->7 so a(7)=4.

%e Sample iteration: 12->18->27->20->30->45->34->51->... so a(12)=12.

%t Table[Min[NestList[If[EvenQ[#],(3#)/2,Floor[(3#+2)/4]]&,n,100]],{n,0,80}] (* _Harvey P. Dale_, May 02 2012 *)

%o (Perl) $|=1; for($n=1;; ++$n){ $m=$n; $d{$m}=$n, $m=f($m) while !$d{$m};

%o (Perl) if ($m<$n){ ($c,$m)=($d{$m},$n); $d{$m}=$c, $m=f($m) while $m >= $n }

%o (Perl) print"$d{$n}," } sub f { $_[0]%2 ? int((3*$_[0]+1)/4) : 3*$_[0]/2 }

%o (PARI) a(n)=local(m); if(n<=0,0,m=n; while((m!=n=(3*n+n%2)\(2+n%2*2))&n<10^99,m=min(m,n)); m)

%Y Cf. A006368, A180853, A028393, A028395.

%K nonn,nice

%O 0,3

%A _N. J. A. Sloane_ and _J. H. Conway_

%E More terms from _Hugo van der Sanden_