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

Zak Seidov zakseidov at mail.ru
Fri Sep 16 07:07:33 CEST 2016

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

>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
>>
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>> Seqfan Mailing list -  http://list.seqfan.eu/
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>
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```