[seqfan] Re: A permutation with divisions

[Charles Greathouse]

Yes, this is a permutation of the positive integers. Suppose not, then
there is some least number which does not occur (since no numbers are
repeated by definition). The last of the numbers occurring before it
appears by some number N, after which point no multiples of the first digit
of the number can occur. But these multiples will occur with all digits 1-9
infinitely often, and so will eventually be picked up regardless of what
initial digits the terms of the sequence after the first N have.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Sat, Jan 25, 2014 at 4:14 AM, Eric Angelini <Eric.Angelini at kntv.be>wrote:

>
> Hello SeqFans,
> I guess this is a nice little permutation
> of the Naturals:
>  a(1)=1
>  a(n+1) is the smallest unused integer
>  that starts with a digit dividing a(n).
>
> S=1,10,2,11,12,3,13,14,7,15,5,16,4,17,18,9,19,100,20,101,102...
>
> Best,
> É.
>
>
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