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A140485
Trajectory of 1 under repeated application of the map: n -> n + second-smallest number that does not divide n.
11
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
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
KEYWORD
nonn
AUTHOR
Eric Angelini, Jun 25 2008
EXTENSIONS
More terms from Stefan Steinerberger, Jul 01 2008
STATUS
approved