A134741 -id:A134741 - cp's OEIS frontend

A134742 Numbers whose square is a permutational number A134640.

0, 1, 15, 50, 85, 195, 327, 561, 789, 867, 1323, 1764, 2450, 2751, 2858, 2878, 3213, 3418, 3538, 4834, 4846, 5062, 5342, 5770, 6286, 7814, 8574, 8634, 9722, 10254, 10610, 10614, 11522, 11702, 11826, 12363, 12543, 13490, 14246, 14502, 14538, 14676, 14818, 14902, 15186, 15434, 15681, 15874, 15963

Offset: 1

Artur Jasinski, Nov 07 2007

nonn

Robert Israel, Table of n, a(n) for n = 1..261

Cf. A134640, A134641, A134642, A134643, A134644, A023811, A134741.

N:= 10^5: # for terms <= N
extend:= proc(x,N,S,b,k)
  local i,R;
  R:= NULL;
  for i in S while x + i*b^k <= N^2 do
    if k = 0 then
       if issqr(x+i*b^k) then R:= R, sqrt(x+i*b^k) fi
    else
       R:= R, procname(x+i*b^k,N,subs(i=NULL,S),b,k-1)
    fi
  od;
  R
end proc:
f:= (b,N) -> extend(0,N,[$0..(b-1)],b,b-1):
R:= 0:
for b from 2 while b^(b-2) < N^2 do
  R:= R, f(b,N);
od:
sort([R]); # Robert Israel, Sep 04 2020

a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[IntegerQ[j^(1/2)], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 7}]; Sqrt[a]

a(n) = sqrt(A134741(n)).

Corrected and more terms from Robert Israel, Sep 04 2020

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

Original entry on oeis.org

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

David Schilling, Dec 13 2020

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.

			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.

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

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

#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 );
        }
    }
}

\\ here ispandig(n) returns base if n is pandigital, otherwise 0.
ispandig(n)={for(b=2, oo, my(r=logint(n,b)+1); if(rAndrew Howroyd, Dec 20 2020

A134745 Numbers which are not permutational numbers A134640.

Original entry on oeis.org

3, 4, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 22, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset: 1

Artur Jasinski, Nov 07 2007

nonn

Cf. A134640, A134641, A134642, A134643, A134644, A134703, A134741, A134742, A134743, A134744.

a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; AppendTo[a, j], {m, 1, Length[w]}], {n, 0, 5}]; c = Table[n, {n, 0, 44790}]; k = Complement[c, a] (*Artur Jasinski*)

cp's OEIS Frontend

A134742 Numbers whose square is a permutational number A134640.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

JAI

PARI

A134745 Numbers which are not permutational numbers A134640.

Views

Author

Keywords

Crossrefs

Programs

Mathematica