[seqfan] Re: Colorless integers
Marc LeBrun
mlb at well.com
Wed Feb 23 04:28:43 CET 2011
Oops, leaped to an unwarranted conclusion at the end, sorry!
========
>="Eric Angelini" <Eric.Angelini at kntv.be>
> (I hope this is not old hat)
I wouldn't knowbut 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=NS if S is odd
> Iterate.
Note that N and S are congruent mod 9.
Therefore when S is odd then NS 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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