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A339693 All pandigital squares which contain each digit exactly once in some base b >= 2. The numbers are written in base 10.

%I A339693 #35 Jan 13 2021 16:09:55
%S A339693 225,38025,314721,622521,751689,3111696,6002500,7568001,10323369,
%T A339693 61058596,73513476,74545956,94517284,105144516,112572100,112656996,
%U A339693 132756484,136936804,181980100,202948516,210308004,211353444,219573124,222069604,230614596,238208356,251983876
%N A339693 All pandigital squares which contain each digit exactly once in some base b >= 2. The numbers are written in base 10.
%C A339693 The sequence consists of all square numbers which when represented in some base b contain all the b digits in that base exactly once.
%C A339693 A225218 has all the squares in base 10 that are pandigital. This sequence is the union of all such sequences in any integer base b >= 2.
%H A339693 David Schilling, <a href="/A339693/b339693.txt">Table of n, a(n) for n = 1..5508</a>
%e A339693 15^2 in base 4 (225 is 3201 in base 4) contains the digits 0-3.
%e A339693 195^2 in base 6 (38025 is 452013 in base 6) contains the digits 0-5.
%e A339693 The next three terms contain all the digits in base 7.
%e A339693 The following four entries are pandigital in base 8, the next 26 in base 9, and so on.
%o A339693 (JAI)
%o A339693 #import "Basic";
%o A339693 dstr := "0123456789abcdef";
%o A339693 main :: () {
%o A339693     digits : [16] int;
%o A339693     for j:2..3_000_000 {
%o A339693         for b:3..16 {
%o A339693             for d : 0..15
%o A339693                 digits[d] = 0;
%o A339693             k := j*j;
%o A339693             s := tprint( "%",  formatInt( k, b ) );
%o A339693             if s.count > b
%o A339693                 continue;
%o A339693             for d : 0..s.count-1 {
%o A339693                 for c : 0..dstr.count-1 {
%o A339693                     if s[d] == dstr[c] {
%o A339693                         digits[c] += 1;
%o A339693                         continue d;
%o A339693                     }
%o A339693                 }
%o A339693             }
%o A339693             for d : 0..b-1 {
%o A339693                 if digits[d] != 1
%o A339693                     continue b;
%o A339693             }
%o A339693             print( "%, ", k );
%o A339693         }
%o A339693     }
%o A339693 }
%o A339693 (PARI) \\ here ispandig(n) returns base if n is pandigital, otherwise 0.
%o A339693 ispandig(n)={for(b=2, oo, my(r=logint(n,b)+1); if(r<b, break); if(r==b && #Set(digits(n,b))==b, return(b))); 0}
%o A339693 for(n=1, 10^5, if(ispandig(n^2), print1(n^2, ", "))) \\ _Andrew Howroyd_, Dec 20 2020
%Y A339693 Cf. A036745, A134741, A258103, A260182, A340501.
%K A339693 nonn,easy,base
%O A339693 1,1
%A A339693 _David Schilling_, Dec 13 2020