OFFSET
1,1
COMMENTS
Terms in this sequence have at least 7 digits in base 6, i.e., are larger than 6^6, since sum(d_i 6^i) = sum(d_i) (mod 5), and 0+1+2+3+4+5 is divisible by 5. So the smallest ones should be of the form "101...." in base 6, where "...." is a permutation of "2345". Actually there is only one such prime, cf. examples.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The smallest base-6 pandigital prime is written "1013425" in base 6.
The next smallest such prime is "1023345"[6]; note that here the "3" is repeated, since there is no such prime of the form "102wxyz" with w=0, 1 or 2. (Using the same reasoning as in the comment, it follows that the (7-digit base-6 pandigital) number has the same parity as the repeated digit, which therefore must be odd to get a prime.)
MATHEMATICA
Select[Range[60000], Min @ DigitCount[#, 6] > 0 && PrimeQ[#] &] (* Amiram Eldar, Apr 13 2021 *)
PROG
(PARI) base(n, b=6)={ local(a=[n%b]); while(0<n\=b, a=concat(n%b, a)); a }
forprime(p=6^6, 6^7, #Set(base(p, 6))==6 & print1(p", "))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, May 30 2010
EXTENSIONS
Edited by Charles R Greathouse IV, Aug 02 2010
STATUS
approved