# [seqfan] Re: Sum divides concatenation

Jack Brennen jfb at brennen.net
Tue Sep 29 21:02:33 CEST 2009

```If zero were allowed, wouldn't it have come earlier in the sequence?

And John Layman's sequence (quoted below) appears to assume that the
sequence is strictly increasing, something which wasn't a condition
of the sequence as originally specified.

zak seidov wrote:
> In this version we have:
> 1,2,6,0,19260,231228,308304,42920,82996,124494,1037450,456478,1244940,...
>
> Zak
>
> --- On Tue, 9/29/09, zak seidov <zakseidov at yahoo.com> wrote:
>
>> From: zak seidov <zakseidov at yahoo.com>
>> Subject: [seqfan] Re: Sum divides concatenation
>> To: "seqfaneu" <seqfan at seqfan.eu>
>> Date: Tuesday, September 29, 2009, 2:06 PM
>>
>> May be you mean a(n)>a(n-1)?
>> Otherwise,  why not a(4)=0:
>> 1+2+6+0=9 and 9|1260?
>> Zak
>>
>> --- On Tue, 9/29/09, John W. Layman <layman at math.vt.edu>
>> wrote:
>>
>>> From: John W. Layman <layman at math.vt.edu>
>>> Subject: [seqfan] Re: Sum divides concatenation
>>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>>> Cc: Eric.Angelini at kntv.be
>>> Date: Tuesday, September 29, 2009, 12:28 PM
>>> Eric Angelini wrote:
>>>> Hello SeqFans,
>>>> I don't know how to find more terms -- thus I
>> don't
>>> know
>>>> if this is old hat in Neil's database:
>>>>
>>>> 1, 2, 6, ...
>>>>
>>>> The sum of the first n integers divides the
>>> concatanion of
>>>> the first n integers; always prolong the seq with
>> the
>>> smal-
>>>> lest _natural_ number not yet used:
>>>>
>>>> 1 divides 1  --> HIT
>>>> 1+2   (=3) divides 12 --> HIT
>>>> 1+2+3 (=6) does not divide 123
>>>> 1+2+4 (=7) does not divide 124
>>>> 1+2+5 (=8) does not divide 125
>>>> 1+2+6 (=9) divides 126 --> HIT
>>>> etc.
>>>>
>>>> Best,
>>>> É.
>>>>
>>>>
>>>>
>>> It takes Mathematica a couple of minutes to get
>>>     {1, 2, 6, 250488, 279786, 1060566, 1414088,
>>> 1767610, 2447460},
>>> which is not in the OEIS.
>>>
>>> Regards,
>>> John
>>>
>>>
>>>
>>>
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>>>
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>>>
>>
>>
>>
>>
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```