# Add to n its second smallest non-divider. Loop

Eric Angelini Eric.Angelini at kntv.be
Wed Jun 25 15:45:12 CEST 2008

```
Could please someone compute a few terms more of:

< Add to n the n-th smallest number not dividing n >

(this is a kind of self-generalization of the rule
herunder)

I've found this first few terms:

S = 1,3,8,20,46,96,...

Best,
É.

(not in the OEIS though 1,3,8,20,46 gives 4 hits)

-----Message d'origine-----
De : Eric Angelini [mailto:Eric.Angelini at kntv.be]
Envoyé : mercredi 25 juin 2008 13:07
À : math-fun; seqfan at ext.jussieu.fr
Objet : Add to n its second smallest non-divider. Loop

Hello MathFun & SeqFans,

Rule:

< Add to n its second smallest non-divider. Loop. >

Is 1 a divider of 7? yes
2                 no
3                 no --> then new n = 7+3 = 10

Is 1 a divider of 10? yes
2                  yes
3                  no
4                  no --> then new n =10+4= 14

Is 1 a divider of 14? yes
2                  yes
3                  no
4                  no --> then new n =14+4= 18

Is 1 a divider of 18? yes
2                  yes
3                  yes
4                  no
5                  no --> then new n =18+5= 23

... etc.

Sequence starting with 7 is: 7,10,14,18,23,...

Sequence starting with 1 is: 1,4,9,13,16,21,...
[not in the OEIS]

Sequence starting with 2 is: 2,6,11,14,18,23,...
[merges with "7-seq"]

Sequence starting with 3 is: 3,7,10,14,...
[merges with "7-seq"]

Sequence starting with 5 is: 5,8,13,16,...
[merges with "1-seq"]

etc.

We might map those sequences like this:

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--+

What number starts the longest sequence containing 2008?
Best,
E.

---

P.-S.

This rule is not very productive:
< Add to n its first smallest non-divider. Loop. >

< Add to n its third smallest non-divider. Loop. >
Etc.

```