A175271 Base-8 pandigital primes.

17119607, 17120573, 17121077, 17127839, 17128931, 17132347, 17135413, 17136029, 17136869, 17148349, 17159479, 17164757, 17181683, 17184119, 17185463, 17185981, 17194171, 17196383, 17196733, 17200373, 17202347

Offset: 1

Author

M. F. Hasler, May 27 2010

Keywords

• nonn
• base

Comments

Base-8 pandigital primes must have at least 9 octal digits, since sum(d_i 8^i) = sum(d_i) (mod 7), and 0+1+...+6+7 is divisible by 7. So the smallest ones should be of the form "10123...." in base 8, where "...." is a permutation of "4567". By chance, the identical permutation already yields a prime: a(1)="101234567" in base-8.

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, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279, A175280.

Programs

PARI

pdp( b=8/*base*/, c=199/* # of terms to produce */) = { my(t, a=[], bp=vector(b,i,b^(b-i))~, offset=b*(b^b-1)/(b-1)); for( i=1,b-1, offset+=b^b; for( j=0,b!-1, isprime(t=offset-numtoperm(b,j)*bp) | next; #(a=concat(a,t))
				

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010