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

2,2

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.

Links

Table of n, a(n) for n=2..14.

Example

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.

Prog

(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++)
}

Crossrefs

Cf. A073643, A116670.

Sequence in context: A105951 A038202 A128415 * A090479 A355559 A227758

Adjacent sequences: A227792 A227793 A227794 * A227796 A227797 A227798

Keyword

nonn,base,less

Author

James G. Merickel, Sep 23 2013

Extensions

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

Status

approved