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

William Keith wjk26 at drexel.edu
Tue Feb 23 18:47:41 CET 2010

> >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.

William Keith

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