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%I #10 Jan 03 2016 10:42:12
%S 105148064265927977839670339,105148064265927977839838717,
%T 105148064265927977839990337,105148064265927977842711099,
%U 105148064265927977843159537,105148064265927977846038379
%N Base-20 pandigital primes: primes having at least one of each digit 0,...,19, when written in base 20.
%C Base-20 pandigital primes must have at least 21 base-20 digits (i.e. they are larger than 20^20 > 10^26), since sum(d_i 20^i) = sum(d_i) (mod 19), and 0+1+...+18+19 is divisible by 19. So the smallest ones should be of the form "10123456789ABCD..." in base 20, where "..." is a permutation of "EFHGIJ" (with A..J representing digits 10..19).
%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.
%o (PARI) pdp( b=20/*base*/, c=99/* # 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-20 expansion of the terms allow one to know up to where it is complete.] You may use a construct of the form: vecextract(pdp(20,999),"1..20")) */
%Y Cf. A138837, A050288, A175271 - A175280.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, May 27 2010
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