A028397 Start at n and iterate the map in A006368; a(n) is the smallest number in the trajectory.

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

Offset: 0

Author

N. J. A. Sloane and J. H. Conway

Keywords

• nonn
• nice

Examples

			Sample iteration: 7->5->4->6->9->7 so a(7)=4.
Sample iteration: 12->18->27->20->30->45->34->51->... so a(12)=12.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006368, A180853, A028393, A028395.

Programs

Mathematica

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

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)

Perl

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

Perl

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

Perl

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

Extensions

More terms from Hugo van der Sanden