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

Zak Seidov zakseidov at mail.ru
Fri Sep 16 16:02:10 CEST 2016

```Also, refs in A046034
to seqfan messages of Charles and David
would be ok, right?

>Пятница, 16 сентября 2016, 15:01 +03:00 от "M. F. Hasler" <oeis at hasler.fr>:
>
>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
>
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>Seqfan Mailing list -  http://list.seqfan.eu/

```