%I #3 Jun 21 2013 16:47:06
%S 10,59,221,441,611,611,611,611,611,611,611,611,611,611,611,611,611,
%T 611,611,611,611,611,611,611,611,611,611,611,611,611,611,611,611,611,
%U 611,611,611,611,611,611,611,611,611,611,611,611,611,611,611,611,611,611
%N Number of nonnegative numbers x < 10^n such that the digits of x^2 occur with an equal frequency of 1.
%e All numbers 0 to 9 have squares containing only digits of frequency 1: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81. See A119509 for the positive terms.
%t cnt = 0; x = 0; Table[While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {1}, cnt++]; x++]; cnt, {n, 5}]
%Y Cf. A119509 (positive terms x), A225428 (for 2 digits).
%K nonn,base
%O 1,1
%A _T. D. Noe_, Jun 21 2013