[seqfan] Re: Colorless integers

Marc LeBrun mlb at well.com
Wed Feb 23 04:15:00 CET 2011


>="Eric Angelini" <Eric.Angelini at kntv.be>
> (I hope this is not old hat)

I wouldn't know--but why do you call this "colorless integers"?

> Let N be an integer
> Let S be the sum of N's digits
> --> make M=N+S if S is even
> --> make M=N-S if S is odd
> Iterate.

Note that N and S are congruent mod 9.

Therefore when S is odd then N-S is divisible by 9.

When S is even then N+S is congruent to 0, 4, 8, 3 or 7 mod 9, as N is
congruent to 0, 2, 4, 6, or 8 respectively.

So each congruence class mod 9 falls into the 0 black hole as follows:
  
          6
          |
          v
         13579 -> 0.
            ^
            |
  2 -> 4 -> 8
 





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