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

225, 38025, 314721, 622521, 751689, 3111696, 6002500, 7568001, 10323369, 61058596, 73513476, 74545956, 94517284, 105144516, 112572100, 112656996, 132756484, 136936804, 181980100, 202948516, 210308004, 211353444, 219573124, 222069604, 230614596, 238208356, 251983876

Offset

1,1

Comments

The sequence consists of all square numbers which when represented in some base b contain all the b digits in that base exactly once.

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.

Links

David Schilling, Table of n, a(n) for n = 1..5508

Example

15^2 in base 4 (225 is 3201 in base 4) contains the digits 0-3.
195^2 in base 6 (38025 is 452013 in base 6) contains the digits 0-5.
The next three terms contain all the digits in base 7.
The following four entries are pandigital in base 8, the next 26 in base 9, and so on.

Prog

(JAI)
#import "Basic";
dstr := "0123456789abcdef";
main :: () {
    digits : [16] int;
    for j:2..3_000_000 {
        for b:3..16 {
            for d : 0..15
                digits[d] = 0;
            k := j*j;
            s := tprint( "%",  formatInt( k, b ) );
            if s.count > b
                continue;
            for d : 0..s.count-1 {
                for c : 0..dstr.count-1 {
                    if s[d] == dstr[c] {
                        digits[c] += 1;
                        continue d;
                    }
                }
            }
            for d : 0..b-1 {
                if digits[d] != 1
                    continue b;
            }
            print( "%, ", k );
        }
    }
}
(PARI) \\ here ispandig(n) returns base if n is pandigital, otherwise 0.
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}
for(n=1, 10^5, if(ispandig(n^2), print1(n^2, ", "))) \\ Andrew Howroyd, Dec 20 2020

Crossrefs

Cf. A036745, A134741, A258103, A260182, A340501.

Sequence in context: A051364 A192934 A264194 * A061051 A036428 A183822

Adjacent sequences: A339690 A339691 A339692 * A339694 A339695 A339696

Keyword

nonn,easy,base

Author

David Schilling, Dec 13 2020

Status

approved