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A175272 Base-12 pandigital primes.

%I A175272 #19 Dec 23 2024 14:53:42
%S A175272 8989787252711,8989787311891,8989787313343,8989787458763,
%T A175272 8989787707627,8989787709211,8989787710927,8989787764211,
%U A175272 8989787806099,8989787810719,8989787959879,8989787974883,8989787992747,8989787999743,8989788058351
%N A175272 Base-12 pandigital primes.
%C A175272 These numbers need to have at least 13 digits in base 12 since any permutation of the digits 0,...,9,A,B will result in a number divisible by 11. For the same reason, it must be digit different from 0 which is repeated. Thus the smallest terms in this sequence are written "10123456....." in base 12, where ..... is a permutation of {7,8,9,A,B}.
%C A175272 Note: Due to the implementation of numtoperm(), the PARI script will not necessarily print the terms in the correct order. In some cases, more than the desired number of terms have to be calculated, and vecsort() to be used to get the correct sequence. - _M. F. Hasler_, May 27 2010
%H A175272 Amiram Eldar, <a href="/A175272/b175272.txt">Table of n, a(n) for n = 1..10000</a>
%H A175272 Alonso Del Arte, <a href="http://oeis.org/wiki/Classifications_of_prime_numbers#By_representation_in_specific_bases">Classifications of prime numbers - By representation in specific bases</a>, OEIS Wiki as of Mar 19 2010.
%H A175272 M. F. Hasler, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2010-March/004070.html">Reply to A. Del Arte's post "Pandigital primes in bases 8,12,..." on the SeqFan list</a>, Mar 19 2010.
%e A175272 8989787252711, 8989787311891, 8989787313343, 8989787458763, ... are written "101234568A79B", "10123456B8A97", "10123456B98A7", "1012345769A8B", ... in base 12 (where A=digit 10, B=digit 11).
%o A175272 (PARI) pdp( b=12/* base */, c=20/* #terms to print */)={ my(t,bp=vector(b,i,b^(b-i))~, offset=b*(b^b-1)/(b-1) /* to fix order of permutations CBA..321 => 012...9AB */); for( i=1,b-1, /* add initial digit */ offset += b^b; for( j=0,b!-1, isprime(t=offset-numtoperm(b,j)*bp) & !print1(t", ") & !c-- & return))}
%Y A175272 Cf. A050288, A138837, A175271, A175273, A175274, A175275, A175276, A175277, A175278, A175279, A175280.
%K A175272 nonn,base
%O A175272 1,1
%A A175272 _M. F. Hasler_, Mar 19 2010
%E A175272 Order of the terms corrected by _M. F. Hasler_, May 27 2010