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A227795 For each base, b, beginning with binary, the number of (b-1)-digit primes with one copy of each digit save one. 0

%I

%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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Last modified January 19 09:12 EST 2021. Contains 340267 sequences. (Running on oeis4.)