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A175278 Base-6 pandigital primes: primes having at least one of each digit 0,1,2,3,4,5 when written in base 6.

%I A175278 #9 Apr 13 2021 07:15:43
%S A175278 48761,50033,50051,50069,50101,50207,50231,50311,50461,51131,51137,
%T A175278 51151,51461,51503,51511,51721,52181,52391,52541,52571,52583,53731,
%U A175278 53881,54091,54121,55001,57191,58481,58901,60161,62591,62921,63029
%N A175278 Base-6 pandigital primes: primes having at least one of each digit 0,1,2,3,4,5 when written in base 6.
%C A175278 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.
%H A175278 Amiram Eldar, <a href="/A175278/b175278.txt">Table of n, a(n) for n = 1..10000</a>
%e A175278 The smallest base-6 pandigital prime is written "1013425" in base 6.
%e A175278 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.)
%t A175278 Select[Range[60000], Min @ DigitCount[#, 6] > 0 && PrimeQ[#] &] (* _Amiram Eldar_, Apr 13 2021 *)
%o A175278 (PARI) base(n,b=6)={ local(a=[n%b]);while(0<n\=b,a=concat(n%b,a));a }
%o A175278 forprime(p=6^6, 6^7, #Set(base(p, 6))==6 & print1(p", "))
%Y A175278 Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175279, A175280.
%K A175278 nonn,base
%O A175278 1,1
%A A175278 _M. F. Hasler_, May 30 2010
%E A175278 Edited by _Charles R Greathouse IV_, Aug 02 2010