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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
0, 3, 1, 9, 52, 283, 2113, 16142, 145227, 1359133, 15000161, 172888810, 2217146126 (list; graph; refs; listen; history; text; internal format)
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 A227758 A304638

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

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Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)