[seqfan] Re: Pandigital primes in bases 8, 12, 16, 20, 36

[Alonso Del Arte]

Max,

Thanks for calculating all those. I hadn't noticed them until yesterday. In
quite a few bases, you spotted smaller pandigital primes than I did. I have
amended the OEIS Wiki page accordingly.

Al

On Fri, Mar 19, 2010 at 8:26 PM, Maximilian Hasler <
maximilian.hasler at gmail.com> wrote:

> Base 12 pandigital primes seem to start with
> 8989787252711, 8989787311891, 8989787313343, 8989787458763,
> 8989787707627, 8989787709211, 8989787710927, 8989788452371,
> 8989787959879, 8989787764211, 8989788261983, 8989787806099,
> 8989787992747, 8989788241699, 8989788262423, 8989787974883,
> 8989787810719, 8989788495007, 8989787999743, 8989788058351, ...
>
> = "101234568A79B", "10123456B8A97", "10123456B98A7", "1012345769A8B",
> "1012345869AB7", "101234586A9B7", "101234586B9A7", "1012345B68A97"...
>
> Now I have a function for any base :)
> pdp(b=12,c=20)={ my(t,offset,bp=vector(b,i,b^(b-i))~);
> forstep(j=1,b-1,1, offset=b*(b^b-1)/(b-1)+j*b^b;
> for(i=0,b!-1, isprime(t=offset-numtoperm(b,i)*bp) & !print1(t", ") &
> !c-- & return))}
>
> Hexa:
> 18528729602926047181, 18528729602926100221, 18528729602926234591,
> 18528729602926112701, 18528729602926235071, 18528729602926108411,
> 18528729602926116331, 18528729602927029471, 18528729602930170831,
> 18528729602928082621, 18528729602930167741, 18528729602928082411,...
>
> = "10123456789ABEFCD", "10123456789ACBEFD", "10123456789AECBDF",
> "10123456789ACEFBD", "10123456789AECDBF", "10123456789ACDEFB"....
>
> base-20:
> 105148064265927977839670339, 105148064265927977839990337,
> 105148064265927977839838717, 105148064265927977848790339,
> 105148064265927977843159537, 105148064265927977846038379,
> 105148064265927977852278397, 105148064265927977848933979,
> 105148064265927977852157937, ...
>
> = "10123456789ABCDEHIFGJ", "10123456789ABCDEJIFGH",
> "10123456789ABCDEIJGFH", "10123456789ABCDHEIFGJ",...
>
> base-36:
> 106474205747327721970821813283682888755465951838540182351,
> 106474205747327721970821813283682888755465951838655934631,
> 106474205747327721970821813283682888755465951838716447391,
> 106474205747327721970821813283682888755465951838776957771,
> 106474205747327721970821813283682888755465951838718031211,
> 106474205747327721970821813283682888755465951838781855251, ...
>
> = "10123456789ABCDEFGHIJKLMNOPQRSTUXYZWV",
> "10123456789ABCDEFGHIJKLMNOPQRSTWUVYXZ",
> "10123456789ABCDEFGHIJKLMNOPQRSTXUWYVZ",
> "10123456789ABCDEFGHIJKLMNOPQRSTYUXWZV", ...
>
> Maximilian
>
> > 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
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
>
>
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