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%I #19 Sep 27 2015 10:29:39
%S 0,3,1,9,52,283,2113,16142,145227,1359133,15000161,172888810,
%T 2217146126
%N For each base, b, beginning with binary, the number of (b-1)-digit primes with one copy of each digit save one.
%C Note that only decimal 2, 11 and 19 are representable in some base using a copy of each digit in that base (base 2 for the first and base 3 for the others), as a number written in base b with a single copy of each digit is congruent to either 0 or (b-1)/2 modulo b-1.
%e In base 3, 10, 12 and 21 are primes: Decimal 3, 5 and 7. In base 4, of the possibilities only 103 is prime: Decimal 19.
%o (PARI) \\ Starts at base 4 and prints in form 'base:count', bases 2 and 3 done by hand.
%o {
%o b=4;while(1,
%o c=0;for(i=1,b!,perm=numtoperm(b,i);
%o if(perm[b-1]!=1,
%o if(gcd(b,perm[1]-1)==1,
%o if(gcd(b-1,perm[b]-1)==1,
%o n=sum(j=1,b-1,(perm[j]-1)*b^(j-1));
%o if(ispseudoprime(n),c++)))));
%o print1(b":"c"\n");b++)
%o }
%Y Cf. A073643, A116670.
%K nonn,base,less
%O 2,2
%A _James G. Merickel_, Sep 23 2013
%E a(14) added by _James G. Merickel_, Oct 14 2013
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