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

0,3

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

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.

Mathematica

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

Prog

(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 }
(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)

Crossrefs

Cf. A006368, A180853, A028393, A028395.

Sequence in context: A105678 A309195 A367026 * A053644 A279170 A292254

Adjacent sequences: A028394 A028395 A028396 * A028398 A028399 A028400

Keyword

nonn,nice

Author

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

Extensions

More terms from Hugo van der Sanden

Status

approved