A227795 - OEIS

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

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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,