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EXAMPLE
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2^66 = {2, 0, 0, 0, 1, 2, 1, 2, 1, 0, 2, 1, 1, 2, 1, 0, 2, 1, 1, 2, 1, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 2, 0, 1}
Count of 1 = count of 2 = count of 0 = 14, than 66 is member
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MATHEMATICA
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Do[If[DigitCount[2^n, 3, 0]==DigitCount[2^n, 3, 1]==DigitCount[2^n, 3, 2], Print[n]], {n, 1, 60000}]
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