A140485 Trajectory of 1 under repeated application of the map: n -> n + second-smallest number that does not divide n.

1, 4, 9, 13, 16, 21, 25, 28, 33, 37, 40, 46, 50, 54, 59, 62, 66, 71, 74, 78, 83, 86, 90, 97, 100, 106, 110, 114, 119, 122, 126, 131, 134, 138, 143, 146, 150, 157, 160, 166, 170, 174, 179, 182, 186, 191, 194, 198, 203, 206, 210, 218, 222, 227, 230, 234, 239, 242, 246

Offset: 1

Author

Eric Angelini, Jun 25 2008

Keywords

• nonn

Examples

			The numbers that do not divide 4 are 3, 5, 6, 7, ..., so a(3) = 4+5 = 9.
Here are the beginnings of the trajectories of some small numbers:
...1--4--9---13--16--21--25--28--32--37--40---
.............|...................|...|
......5--8---+...............29--+...|
.....................................|
...2--6--11--14--18--23--26--30------+
.............|...........|...........|
...3--7--10--+...........|.......33--+
.........................|
.............12--19--22--+
.................|.......|
.............15--+.......|
.........................|
.................17--20--+
..............................................
.........................24--31--34--38--42---
.............................|.......|
.........................27--+...35--+
		

Crossrefs

Cf. A140486, A140487, A140488, A140489, A140595.

Programs

Mathematica

f[n_] := (k = 1; s = {}; While[ True, k++; If[ !Divisible[n, k], AppendTo[s, k]]; If[Length[s] == 2, Break[]]]; n + Last[s]); NestList[f, 1, 58] (* Jean-François Alcover, Oct 05 2011 *)
NestList[#+Complement[Range[100],Divisors[#]][[2]]&,1,60] (* Harvey P. Dale, Apr 27 2012 *)

Extensions

More terms from Stefan Steinerberger, Jul 01 2008