A202170 Numbers k such that k^2 has only digits 0, 4 and 8.

0, 2, 20, 22, 200, 202, 220, 298, 2000, 2002, 2020, 2022, 2200, 2202, 2980, 20000, 20002, 20020, 20022, 20200, 20220, 22000, 22002, 22020, 28998, 29800, 200000, 200002, 200020, 200022, 200200, 200202, 200220, 202000, 202002, 202200, 220000, 220002, 220020, 220200, 289980, 298000, 632522, 2000000

Offset: 1

Author

M. F. Hasler, Dec 13 2011

Keywords

• nonn
• base

Comments

k = 2*m where m^2 has only digits 0, 1 and 2. - Robert Israel, Jul 17 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..204

Crossrefs

Cf. A030097, A058441.

Includes 2*A136808.

Programs

Magma

[ n: n in [0..10^6 by 2] | Set(Intseq(n^2)) subset [0,4,8] ]; // Bruno Berselli, Dec 19 2011

Maple

Res:= NULL:
for x from 0 to 3^12 do
  L:= convert(x,base,3);
  y:= add(L[i]*10^(i-1),i=1..nops(L));
  if issqr(y) then
    Res:= Res, 2*sqrt(y)
  fi
od:
Res; # Robert Israel, Jul 17 2018

Mathematica

Select[Sqrt[FromDigits[#]]&/@Tuples[{0,4,8},13],IntegerQ] (* Harvey P. Dale, Sep 08 2024 *)

PARI

is_A202170(n)=!setminus(Set(Vec(Str(n^2))),Vec("048"))

Extensions

More terms from Robert Israel, Jul 17 2018