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%I #20 Jan 02 2023 12:30:47
%S 17119607,17120573,17121077,17127839,17128931,17132347,17135413,
%T 17136029,17136869,17148349,17159479,17164757,17181683,17184119,
%U 17185463,17185981,17194171,17196383,17196733,17200373,17202347
%N Base-8 pandigital primes
%C 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.
%H Amiram Eldar, <a href="/A175271/b175271.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 M. F. Hasler, <a href="http://list.seqfan.eu/oldermail/seqfan/2010-March/004069.html">Reply to A. Del Arte's post "Pandigital primes in bases 8,12,..." on the SeqFan list</a>, Mar 19 2010.
%o (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")) */
%Y Cf. A050288, A138837, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175279, A175280.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, May 27 2010
%E Edited by _Charles R Greathouse IV_, Aug 02 2010
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