%I
%S 138,648,701,951,1007,1070,1380,1393,3153,3451,3743,3747,4462,6357,
%T 6480,7001,7010,7071,9510,9701,10007,10070,10097,10243,10538,10700,
%U 13800,13930,20247,20347,22138,31530,34510,37430,37470,37538,38071,38602,44620,63357,63403,63570,64800
%N Integers n such that the digit set of n^2 is {0,1,4,9}.
%C n cannot end in the decimal digits 4, 5 or 6; but it most often ends in 0 since if n is present so is 10*n.
%C n cannot start with the decimal digits 5 or 8. It usually starts with either 3 or 1.
%C n must lie between 1*10^k & sqrt(2)*10^k, 2*10^k & sqrt(5)*10^k, 3 & sqrt(12)*10^k, sqrt(14)*10^k & sqrt(15)*10^k, sqrt(19)*10^k & sqrt(20)*10^k, sqrt(40)*10^k & sqrt(45)*10^k, sqrt(49)*10^k & sqrt(50)*10^k, sqrt(90)*10^k & sqrt(92)*10^k, sqrt(94)*10^k & sqrt(95)*10^k, sqrt(99)*10^k & sqrt(100)*10^k; for k>0.
%e 138 = 19044 which has only the decimal digits 0, 1, 4 & 9. Therefore it is in the sequence.
%t fQ[n_] := Union[IntegerDigits[n^2]] == {0, 1, 4, 9}; Select[ Range@ 65000, fQ]
%o (PARI) isok(n) = Set(digits(n^2)) == [0, 1, 4, 9]; \\ _Michel Marcus_, Aug 01 2018
%Y Cf. A285550, A316969.
%K base,nonn
%O 1,1
%A _Robert G. Wilson v_, Jul 31 2018
