A175272 Base-12 pandigital primes.

8989787252711, 8989787311891, 8989787313343, 8989787458763, 8989787707627, 8989787709211, 8989787710927, 8989787764211, 8989787806099, 8989787810719, 8989787959879, 8989787974883, 8989787992747, 8989787999743, 8989788058351

Offset: 1

Author

M. F. Hasler, Mar 19 2010

Keywords

• nonn
• base

Comments

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}.

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

Examples

			8989787252711, 8989787311891, 8989787313343, 8989787458763, ... are written "101234568A79B", "10123456B8A97", "10123456B98A7", "1012345769A8B", ... in base 12 (where A=digit 10, B=digit 11).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Alonso Del Arte, Classifications of prime numbers - By representation in specific bases, OEIS Wiki as of Mar 19 2010.
• M. F. Hasler, Reply to A. Del Arte's post "Pandigital primes in bases 8,12,..." on the SeqFan list, Mar 19 2010.

Crossrefs

Cf. A050288, A138837, A175271, A175273, A175274, A175275, A175276, A175277, A175278, A175279, A175280.

Programs

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))}

Extensions

Order of the terms corrected by M. F. Hasler, May 27 2010