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

[Maximilian Hasler]

Please note that some of the terms in that message of mine were not in order,
but I think I corrected the errors I may have introduced temporarily in the OEIS
by extending and/or submitting the corresponding sequences.

Maximilian

On Wed, Aug 25, 2010 at 5:56 PM, Alonso Del Arte
<alonso.delarte at gmail.com> wrote:
> 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
>> >>
>> >> _______________________________________________
>> >>
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>> >>
>> >
>>
>>
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