[seqfan] Re: Pandigital primes in bases 8, 12, 16, 20, 36
Maximilian Hasler
maximilian.hasler at gmail.com
Sat Mar 20 01:04:13 CET 2010
The numbers
17119607, 17120573, 17121077, 17135413, 17136869, 17127839, 17136029,
17132347, 17128931, 17148349, 17213239, 17245999, 17246951, 17247973,
17181683, 17213939, 17247203, 17159479, 17184119, 17200373, 17196383,
17253727, 17253853, 17286557, 17257759, 17265949, 17185463, 17185981,
17196733, 17229479, 17229983, 17194171, 17202347, 17287859, 17235107,
17164757, 17202389, 17258711, 17223571, 17288083, 17292563, 17348983,
17349949, 17349991, 17352623, 17352637, 17360701, 17353967, 17365237,
17361247, 17361373,...
seem to be base-8 pandigital primes.
These are maybe not the smallest, I created them by appending a
permutation of digits 0..7 to a given (most significant) digit (0 =>
no prime, since these numbers are divisible by 7; 1 => yields the
above primes, 2=> ?,...)
In base 8 they read
"101234567", "101236475", "101237465", "101273465", "101276345",
"101254637", "101274635", "101265473", "101256743", "101324675",
"101523467", "101623457", "101625347",...
Maximilian
PS: cryptic PARI code:
{c=0; p8=vector(8,i,8^(8-i))~; forstep(j=0,7,1,
offset=8*(8^8-1)/7+j*8^8; for(i=0,8!-1,
isprime(t=offset-numtoperm(8,i)*p8) & !print1(t", ") & c++>50 &
return))}
On Sat, Mar 20, 2010 at 12:02 AM, Alonso Del Arte
<alonso.delarte at gmail.com> wrote:
> If it interests anyone, I am slightly curious to find out a few pandigital
> primes in bases 8, 12, 16, 20, 36. I just got done adding
> http://oeis.org/wiki/Classifications_of_prime_numbers#By_representation_in_specific_bases
> There
> are other calculations I'm much more interested in, but I have to admit I do
> care a tiny bit to know the answer to this one. There is also the
> interesting issue of representing such large numbers in a compact manner. In
> the case of the third vigesimal Smarandache-Wellin prime, I searched long
> and hard for a concise way to express it in the form x^y - r, but to no
> avail.
>
> Of the various sequences listed in that new section which are not already in
> the OEIS as A-numbered sequences, the only one which I would consider worth
> submitting is the sequence of binary Smarandache-Wellin primes, and even
> that only after further study and after Neil's vacation. But if any of y'all
> find anything interesting in the others, I hope you'd share it in this list.
>
> Al
>
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