# [seqfan] Re: Another "interpret this sequence!" brainteaser

Charles Greathouse charles.greathouse at case.edu
Tue Aug 3 03:03:40 CEST 2010

```> The sequence seems to count n-digit primes (in decimal notation) which have
> no digit 0 and no repeated digits.

Ah.  That seems to explain it, though I get a(8) = 23082 where the
author has 55440.  a(8) has to be the last term, since 0-free 9-digit
primes must have repeated decimal digits or they'd be divisible by 9.

> We did this one back in May. :^)

Sorry, I missed that!  I see now that both of the issues I raise above
have been discussed.

I'll submit changes to the sequence since I suppose no one else did then.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Aug 2, 2010 at 6:40 PM, Alois Heinz <heinz at hs-heilbronn.de> wrote:
> The sequence seems to count n-digit primes (in decimal notation) which have
> no digit 0 and no repeated digits.
>
> keywords: base, fini, ...
>
> "pandigital" in description is misleading
>
> Charles Greathouse schrieb:
>> A140532 is "a(n) = number of n-digit pandigital primes."  In the
>> examples, it considers all primes below 100 *except* 11 to be
>> pandigital.
>>
>> The first interpretation that came to mind was that the sequence was
>> counting primes without repeated digits.  But this gives |{103, ...,
>> 983}| = 97 for a(3), while the sequence has 83.  (There are 143
>> 3-digit primes, so it's leaving out 60.)
>>
>> Any ideas?  The sequence cites
>> Clifford A. Pickover, Wonders of Numbers.
>> Schaum's Outlines, Combinatorics, see inclusion/exclusion principle
>> as references, but I don't think the sequence appears in either, based
>> on a Google Book search.
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>
>
>
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>

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