[seqfan] Re: Help with a(n) and a cumulative sum

[jean-paul allouche]

Dear Neil, dear all

Yes it looks like a topological argument should make it. (But
it is not really clear to me [yet] how to do this.)

best wishes
jean-paul

Le 15/07/2019 à 05:53, Neil Sloane a écrit :
> Robert,  I was just looking at A309151, as it happens.  Could you add your
> sequence 1, 6, 4, 66, 34, 666, 334, ... to the OEIS please?  It is a useful
> data point.
>
> Is A309151 going to need an argument from topology to show that it exists
> (thus proving I was wrong when I said it was not deep!) ?  Jean-Paul?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
>
> On Sun, Jul 14, 2019 at 11:29 PM <israel at math.ubc.ca> wrote:
>
>> There are infinite sequences such that a(n) doesn't share any digit with
>> the cumulative sum. For example: 1, 6, 4, 66, 34, 666, 334, ... with
>> cumulative sums 1, 7, 11, 77, 111, 777, 1111, ... So your sequence A309151
>> can indeed be infinite.
>>
>> Cheers,
>> Robert
>>
>> On Jul 14 2019, Éric Angelini wrote:
>>
>>> Hello SeqFans, Here is the draft of a strange sequence:
>>> https://oeis.org/draft/A309151 It says: Lexicographically earliest
>>> sequence of different terms starting with a(1) = 1 such that a(n)
>> doesn't
>>> share any digit with the cumulative sum a(1) + a(2) + a(3) + ... +
>> a(n-1)
>>> + a(n). And in the Comments section: As this sequence needs a lot of
>>> backtracking, we don't guarantee the accuracy of the last 79 integers of
>>> the 1079-term b-file. Indeed, the problem comes from the fact that some
>>> cumulative sums quickly block the extension of the sequence. This is the
>>> case with 10 (or any other sum ending in zero). But this is the case too
>>> with 301 after
>>> 1,2,3,5,4,6,7,8,9,10,11,12,14,22,20,23,24,30,13,15,16,18,28. So, we
>>> bumped quite often in a "bad sum" (on the average, the sequence was
>>> extended by 100 terms for every backtrack). To make a prior list of "bad
>>> sums" is difficult (meaning impossible, I guess): 258002 is such a "bad
>>> sum" if you have previously used {1,3,4,6,7,9,39,49,69,79} else 258002 +
>>> 79 = 258081 would be ok. So my questions are: could the sequence be
>>> infinite? Could a list of "bad sum numbers" be easely defined and used?
>>> Post-scriptum: I am working, together with Jean-Marc, on the variants:
>>> "Lexicographically [...] such that a(n) shares exacly k digit with the
>>> cumulative sum a(1) + a(2) + a(3) + ... + a(n-1) + a(n)", with k = 1, 2,
>>> 3, ... Best, É.
>>>
>>> --
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
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