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

[Neil Sloane]

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.
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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.
> >
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> >
> >
>
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