[seqfan] Re: Playing with dividing by concatenations

[Neil Sloane]

Daniel Sherman, Yes, those are interesting - please do submit them!

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 Mon, Apr 9, 2018 at 5:46 AM, Daniel via SeqFan <seqfan at list.seqfan.eu>
wrote:

> Hi all,
> I recently added a cross-reference between https://oeis.org/A029455 in
> which n divides the concatenation of all numbers <=n, and
> https://oeis.org/A171785, in which n divides the concatenation of all
> a(1), a(2), ... a(n).
> I then decided to look for the next obvious types of
> concatenation-dividing sequences: those in which n itself is *not* included
> in the concatenation. For these you'd obviously need to start with defining
> a(1)=1 and a(2)=2, but the sequence would then go as follows:
>
>    - A029455-equivalent, in which n divides the concatenation of all
> numbers < n: 1, 2, 3, 9, 27...
>    - A171785-equivalent, in which n strictly increases and divides the
> concatenation of all terms a(1) through a(n-1): 1, 2, 3, 41, 43, 129,
> 9567001, 21147541, 22662659, 23817877,  24837187, 28850377, 28872229,
> 37916473, 48749751.
>
>
> Unless I've made a mistake, I can't find either of these in the database.
> The closest I found is A240588, in which n divides the concatenation of all
> terms a(1) through a(n-1) but does *not* strictly increase, rather only
> defines that n cannot have yet appeared earlier in the sequence. (I will
> add cross-references to this one. I like cross-references.)
>
> Are these two sequences worth adding? Someone else will have to expand the
> A029455-equivalent beyond the first few (fairly useless) terms, because the
> next term requires a concatenation too long for Wolfram Alpha to handle,
> and I'm just a dabbler so I don't have dedicated mathematics software for
> doing this sort of thing. But it was able to get quite a few terms of the
> A171785-equivalent, and can add that one myself.
>
> Daniel Sterman
>
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