[seqfan] Re: Naturals reordered: a(n)th first digit is not a(n)thdigitof S

[Eric Angelini]

Hello William,
I am not sure that I understand your point:
- are you saying that an infinite sequence is possible
  with the rule: 
  "Build the Z sequence using always the smallest integer 
   not used so far"
- or are you saying that my wording is ambiguous as it
  would be possible to build a finite sequence _with no
  holes_ (that is with all integers 1,2,3,4,.... n 
  n being the last possible one (which was my intent)
Anyway I must admit that my original phrasing is poor...
Best,
É.



-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] De la part de William Keith
Envoyé : mardi 23 février 2010 18:48
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Naturals reordered: a(n)th first digit is not a(n)thdigitof S

> >This suggests the ultimate Z sequence:
> > « First lexically re-ordering Z of the Naturals where
> >   no digit of a(n) is the a(n)th digit of Z »
> >But this is impossible, Z has to stop somewhere: we have
> >no more choice for the 1023456789th digit of Z, for instance...  

> ... How many terms are in Z?
> ... What would be the last term?

> A short explanation: if 2106515 is in Z, this means that no
> digit of 2106515 (2,1,0,6 or 5) is the 2106515th digit of Z.

> Best,
> É.

Rather than Z stopping, I think "the lexically smallest number such that no digit of a(n) is the a(n)th digit of Z" would simply not be a reordering of the naturals.  One could continue producing terms, but 1023456789 would never be an element of the sequence.

Cordially,
William Keith


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