# [seqfan] Re: Dividing the sum of the k leftmost digits of N by k

Tanya Khovanova mathoflove-seqfan at yahoo.com
Wed Aug 26 20:02:04 CEST 2009

```A ten digit number like that exists, and it is unique. I forgot what it is, but I can find it if I have time:
http://blog.tanyakhovanova.com/?p=31

I believe Martin Gardner wrote about it.

--- On Wed, 8/26/09, Eric Angelini <Eric.Angelini at kntv.be> wrote:

> From: Eric Angelini <Eric.Angelini at kntv.be>
> Subject: [seqfan]  Dividing the sum of the k leftmost digits of N by k
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Wednesday, August 26, 2009, 1:04 PM
>
> Hello SeqFans, [idea coming from the recent 'average' post
> by Zakir]
>
> is 978015 the biggest number N with no two same digits
> having the pro-
> perty that when the sum of the k leftmost digits of N is
> divided by k
> the result is always an integer?
>
>
>
>    N = 978015
>
> - dividing the sum of the 2 leftmost digits by 2: (9+7)/2 =
> 8
> - dividing the sum of the 3 leftmost digits by 3: (9+7+8)/3
> = 8
> - dividing the sum of the 4 leftmost digits by 4:
> (9+7+8+0)/4 = 6
> - dividing the sum of the 5 leftmost digits by 5:
> (9+7+8+0+1)/5 = 5
> - dividing the sum of the 6 leftmost digits by 6:
> (9+7+8+0+1+5)/6 = 5
>
> Many seq based on this idea could be added to the OEIS (if
> of interest)
>
> The same with the rightmost digits.
>
> (see http://www.research.att.com/~njas/sequences/A061383
>      "Arithmetic mean of digits is an
> integer.")
> Best,
> É.
>
>
>
>
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>
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>

```