# [seqfan] Re: Derangements of N? Integers sharing digits with ranks

Charles Greathouse charles.greathouse at case.edu
Fri Jul 30 18:22:25 CEST 2010

```Surely both are finite, and thus not in bijection with N at all, let
alone derangements?  Consider, e.g., a(102345678).

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Jul 30, 2010 at 12:13 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
>
> Smallest positive integer a(n) not yet in the sequence S and sharing
> no digit with n or (n+1) in its decimal representation:
>
> n = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25...
> S = 3,1,2,6,4,5,9,7,8,22,30,40,20,23,24,25,26,27,33,34,35,10,11,13,...
>
> -----------------------
> Smallest positive integer a(n) not yet in the sequence T and sharing
> no digit with n, (n-1) or (n+1) in its decimal representation:
>
> n = 1,2,3,4,5,6,7,8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25...
> T = 3,4,1,2,7,8,5,6,22,23, 9,40,50,20,27,24,25,26,33,34,35,10,11,16,...
> -----------------------
>
> Are S and T (here computed by hand) derangements of N?
> Best,
> É.
>
> Xref:
> http://www.research.att.com/~njas/sequences/A096779
> "Smallest number not occurring earlier having no common digits
>  with n in its decimal representation."
>
>
>
>
>
>
>
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>
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>

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