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

1,1

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.

Prog

(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))<c | return(vecsort(a))))} /* NOTE: Due to the implementation of numtoperm, the returned list may be incomplete towards its end. Thus computation of more than the required # of terms is recommended. [The initial digits of the base-8 expansion of the terms allow one to know up to where it is complete.] You may use a construct of the form: vecextract(pdp(8, 999), "1..30")) */

Crossrefs

Cf. A050288, A138837, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279, A175280.

Sequence in context: A043680 A204673 A205640 * A172597 A172569 A254000

Adjacent sequences: A175268 A175269 A175270 * A175272 A175273 A175274

Keyword

nonn,base

Author

M. F. Hasler, May 27 2010

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved