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

Tanya Khovanova mathoflove-seqfan at yahoo.com
Wed Aug 26 23:12:13 CEST 2009

```Yes, I meant that.

--- On Wed, 8/26/09, Ignacio Larrosa Cañestro <ilarrosa at mundo-r.com> wrote:

> From: Ignacio Larrosa Cañestro <ilarrosa at mundo-r.com>
> Subject: [seqfan] Re: 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, 4:46 PM
> Tanya Khovanova wrote:
> > I am very sorry.
> >
> > I confused it with another problem: the number formed
> by the first k
> > integers is divisible by k.
> >
>
> Do you meant 381654729(0)?
>
> Saludos,
>
> Ignacio Larrosa Cañestro
> A Coruña (España)
> ilarrosa at mundo-r.com
>
> > --- On Wed, 8/26/09, Robert Israel <israel at math.ubc.ca>
> wrote:
> >
> >> From: Robert Israel <israel at math.ubc.ca>
> >> Subject: [seqfan] Re: 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, 2:32 PM
> >> It can't exist, since for k=10,
> >> 0+1+...+9 = 45 is not divisible by 10.
> >> Moreover, if my Maple program is to be believed,
> there are
> >> none with 8 or
> >> 9 digits. However, there are 15 with 7 digits:
> >> 1502794
> >> 1506394
> >> 1560394
> >> 2015794
> >> 4839605
> >> 4893605
> >> 4897205
> >> 5102794
> >> 5106394
> >> 5160394
> >> 7984205
> >> 8439605
> >> 8493605
> >> 8497205
> >> 9784205
> >>
> >> Cheers,
> >> Robert Israel
> >>
> >> On Wed, 26 Aug 2009, Tanya Khovanova wrote:
> >>
> >>> 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.
> >>>>
> >>>>
> >>>>
> >>>>
> >>>>
> _______________________________________________
> >>>>
> >>>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>>
> >>>
> >>>
> >>>
> _______________________________________________
> >>>
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
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> >
> >
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> >
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```