# [seqfan] Re: A259444

Neil Sloane njasloane at gmail.com
Mon Oct 26 18:56:44 CET 2015

```In private email, Vladimir and I have straightened out the problem.

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.
Email: njasloane at gmail.com

On Mon, Oct 26, 2015 at 4:48 AM, Vladimir Shevelev <shevelev at bgu.ac.il>
wrote:

> Thank you, Neil, for the explanation.
> However, in A259444, for, say, a(3)=5 we should
> have for m,r<3,  5 != a(m)^a(r) which
> is not true. I think that the name could be
>
> a(1)=2. If we already have the terms a(1)<a(2)<
> ...<a(n), then a(n+1) is the smallest number >a(n)
> which has no the form a(i)^a(j), i,j<=n.
>
>
> Best regards,
>
> ________________________________________
> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Neil Sloane [
> njasloane at gmail.com]
> Sent: 25 October 2015 17:54
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: A259444
>
> It looks like ^ is exponentation, which is what it always is
>
> After 2, we have to avoid 2^2 = 4, so 3 works
>
> After 2,3 we have to avoid 2^2=4, 2^3=8, 3^2=9, 3^3=27, so 5 works,
> also 6, also 7. Then 10, 11 and so on
>
> I will add some examples to the sequence
>
> 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.
> Email: njasloane at gmail.com
>
>
> On Sun, Oct 25, 2015 at 10:58 AM, Vladimir Shevelev <shevelev at bgu.ac.il>
> wrote:
>
> > I do not understand the definition of A259444:
> > "a(1)=2. For n>1, a(n) = smallest number > a(n-1)
> > such that, for all m,r<n, a(n) != a(m)^a(r)."
> > The first terms 2, 3, 5, 6, 7, 10,...
> >
> > Most likely, the author meant under ^ another operation.
> > But + is not suitable: indeed, if a(n) != a(m)+a(r), then
> > a(6)=10 is not suitable, since for m=2, r=5 we have a(m)+a(r)=a(6)
> > and also for m=3, r=3 we also have a(m)+a(r)=a(6).
> > What is the right definition?
> >
> > Best regards,
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
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>
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>
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>
```