A257763 Zeroless numbers n such that n and n^2 have the same set of decimal digits.

1, 4762, 4832, 12385, 14829, 26394, 34196, 36215, 49827, 68474, 72576, 74528, 79286, 79836, 94583, 94867, 96123, 98376, 123385, 123546, 124235, 124365, 124579, 124589, 125476, 125478, 126969, 129685, 135438, 139256, 139261, 139756, 149382, 152385, 156242

Offset: 1

Author

Alois P. Heinz, May 07 2015

Keywords

• nonn
• base

Examples

			4762 is in the sequence because it is zeroless and 4762^2 = 22676644 has the same set of decimal digits as 4762: {2,4,6,7}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A029793, A052382, A257760.

Programs

Maple

a:= proc(n) option remember; local k, s;
      for k from 1+`if`(n=1, 0, a(n-1)) do
        s:= {convert(k, base, 10)[]};
        if not 0 in s and s={convert(k^2, base, 10)[]}
           then return k fi
      od
    end:
seq(a(n), n=1..10);

Mathematica

sameQ[n_]:=Union[IntegerDigits[n]]==Union[IntegerDigits[n^2]];Select[Range@156242,And[FreeQ[IntegerDigits[#],0],sameQ[#]]&] (* Ivan N. Ianakiev, May 08 2015 *)

PARI

isok(n) = vecmin(d=digits(n)) && Set(d) == Set(digits(n^2)); \\ Michel Marcus, May 31 2015

Python

A257763_list = [n for n in range(1,10**6) if not '0' in str(n) and set(str(n)) == set(str(n**2))] # Chai Wah Wu, May 31 2015

Formula

{A029793} intersect {A052382}.