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

0, 3, 1, 9, 52, 283, 2113, 16142, 145227, 1359133, 15000161, 172888810, 2217146126

Offset: 2

Author

James G. Merickel, Sep 23 2013

Keywords

• nonn
• base
• less

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A073643, A116670.

Programs

PARI

\\ Starts at base 4 and prints in form 'base:count', bases 2 and 3 done by hand.
{
b=4;while(1,
c=0;for(i=1,b!,perm=numtoperm(b,i);
if(perm[b-1]!=1,
if(gcd(b,perm[1]-1)==1,
if(gcd(b-1,perm[b]-1)==1,
n=sum(j=1,b-1,(perm[j]-1)*b^(j-1));
if(ispseudoprime(n),c++)))));
print1(b":"c"\n");b++)
}

Extensions

a(14) added by James G. Merickel, Oct 14 2013