Add to n its second smallest nondivider. 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 nth smallest number not dividing n >
(this is a kind of selfgeneralization 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 : mathfun; seqfan at ext.jussieu.fr
Objet : Add to n its second smallest nondivider. Loop
Hello MathFun & SeqFans,
Rule:
< Add to n its second smallest nondivider. Loop. >
Let's start with n = 7, for instance
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 "7seq"]
Sequence starting with 3 is: 3,7,10,14,...
[merges with "7seq"]
Sequence starting with 5 is: 5,8,13,16,...
[merges with "1seq"]
etc.
We might map those sequences like this:
1491316212528323740 ...
  
58+ 29+ 

26111418232630+
  
3710+  33+

121922+
 
15+ 

1720+
2431343842 ...
 
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 nondivider. Loop. >
What about:
< Add to n its third smallest nondivider. Loop. >
Etc.
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