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Number of nonnegative numbers x < 10^n such that the digits of x^2 occur with an equal frequency of 1.
2

%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