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

1,2

Links

Table of n, a(n) for n=1..59.

Example

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--+

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 *)

Crossrefs

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

Sequence in context: A141000 A312878 A312879 * A312880 A312881 A312882

Adjacent sequences: A140482 A140483 A140484 * A140486 A140487 A140488

Keyword

nonn

Author

Eric Angelini, Jun 25 2008

Extensions

More terms from Stefan Steinerberger, Jul 01 2008

Status

approved