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

%I A202170 #24 Jul 08 2025 14:35:52
%S A202170 0,2,20,22,200,202,220,298,2000,2002,2020,2022,2200,2202,2980,20000,
%T A202170 20002,20020,20022,20200,20220,22000,22002,22020,28998,29800,200000,
%U A202170 200002,200020,200022,200200,200202,200220,202000,202002,202200,220000,220002,220020,220200,289980,298000,632522,2000000
%N A202170 Numbers k such that k^2 has only digits 0, 4 and 8.
%C A202170 k = 2*m where m^2 has only digits 0, 1 and 2. - _Robert Israel_, Jul 17 2018
%H A202170 Robert Israel, <a href="/A202170/b202170.txt">Table of n, a(n) for n = 1..204</a>
%p A202170 Res:= NULL:
%p A202170 for x from 0 to 3^12 do
%p A202170   L:= convert(x,base,3);
%p A202170   y:= add(L[i]*10^(i-1),i=1..nops(L));
%p A202170   if issqr(y) then
%p A202170     Res:= Res, 2*sqrt(y)
%p A202170   fi
%p A202170 od:
%p A202170 Res; # _Robert Israel_, Jul 17 2018
%t A202170 Select[Sqrt[FromDigits[#]]&/@Tuples[{0,4,8},13],IntegerQ] (* _Harvey P. Dale_, Sep 08 2024 *)
%o A202170 (PARI) is_A202170(n)=!setminus(Set(Vec(Str(n^2))),Vec("048"))
%o A202170 (Magma) [ n: n in [0..10^6 by 2] | Set(Intseq(n^2)) subset [0,4,8] ]; // _Bruno Berselli_, Dec 19 2011
%Y A202170 Cf. A030097, A058441.
%Y A202170 Includes 2*A136808.
%K A202170 nonn,base
%O A202170 1,2
%A A202170 _M. F. Hasler_, Dec 13 2011
%E A202170 More terms from _Robert Israel_, Jul 17 2018