[seqfan] Re: both n and n^2 use just digits (2,3,5,7}

M. F. Hasler oeis at hasler.fr
Fri Sep 16 14:01:08 CEST 2016

```On Fri, Sep 16, 2016 at 1:07 AM, Zak Seidov via SeqFan <
seqfan at list.seqfan.eu> wrote:

> Thanks to Charles and David!
> Worth submitting as bref?
> zak
>

It has already been submitted as A153025 <https://oeis.org/A153025> in 2008
but I think a comment in
A046034 <https://oeis.org/A046034> Numbers whose digits are primes.
In any case, the respetive xrefs should have been there, but weren't...

-Maximilian

>
> >Пятница, 16 сентября 2016, 7:33 +03:00 от "David Wilson" <
> davidwwilson at comcast.net>:
> >
> >5, 235, and 72335 are the only such numbers <= 31 digits.
> >I suspect there is a probabilistic argument that the number of such
> numbers is finite, and the probability of the existence of such a number
> with >= 32 digits is extremely small.
> >The only methods I know for categorically solving this question involve
> showing that for sufficient d, if a number n consists of d good digits,
> then n^2 either cannot start with d good digits or end with d good digits.
> These arguments do not work for the set of digits {2,3,5,7}.
> >So the answer to your question is almost certainly yes, but I doubt we'll
> ever prove it.
> >
> >> -----Original Message-----
> >> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Zak
> >> Seidov via SeqFan
> >> Sent: Monday, August 15, 2016 7:35 AM
> >> To: Sequence Fanatics Discussion list
> >> Cc: Zak Seidov
> >> Subject: [seqfan] both n and n^2 use just digits (2,3,5,7}
> >>
> >>  Are {5,235,72335}
> >> the only numbers n
> >> such that  both n and n^2 use just digits (2,3,5,7}?
> >> Cf. A191486, A275971.
> >> zak
> >>
> >> --
> >> Seqfan Mailing list -  http://list.seqfan.eu/
> >
> >
> >--
> >Seqfan Mailing list -  http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Maximilian
```