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A175279 Base-7 pandigital primes: primes having at least one of each digit 0,...,6 when written in base 7.

%I A175279 #8 Apr 13 2021 07:16:34
%S A175279 863231,863279,863867,863897,864203,864251,865379,865871,865877,
%T A175279 866011,866399,866653,866693,867641,867719,868033,868069,868081,
%U A175279 868103,868121,868123,868327,868423,868453,868669,868787,868793,868801,868943,868999
%N A175279 Base-7 pandigital primes: primes having at least one of each digit 0,...,6 when written in base 7.
%C A175279 Terms in this sequence have at least 8 digits in base 7, i.e., are larger than 7^7, since sum(d_i 7^i) = sum(d_i) (mod 6), and 0+1+2+3+4+5+6 is divisible by 3. So there must be at least one repeated digit, which may not be 0 nor 6 neither odd (else the resulting number is even). The smallest terms are therefore of the form "1022...." in base 7, where "...." is a permutation of "3456", cf. examples.
%H A175279 Amiram Eldar, <a href="/A175279/b175279.txt">Table of n, a(n) for n = 1..10000</a>
%e A175279 The smallest base-7 pandigital primes are "10223465", "10223564", "10225364", "10225436", "10226354" and "10226453", written in base 7.
%t A175279 Select[Range[10^6], Min @ DigitCount[#, 7] > 0 && PrimeQ[#] &] (* _Amiram Eldar_, Apr 13 2021 *)
%o A175279 (PARI) base7(n)={ local(a=[n%7]);while(0<n\=7,a=concat(n%7,a));a }
%o A175279 forprime(p=7^7, 7^7*1.1, #Set(base7(p))==7 & print1(p", "))
%Y A175279 Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175277, A175278, A175280.
%K A175279 nonn,base
%O A175279 1,1
%A A175279 _M. F. Hasler_, May 30 2010
%E A175279 Edited by _Charles R Greathouse IV_, Aug 02 2010