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Let f(x) = x^n where n is a fixed positive integer and x =1, 2, \cdots . Is the decimal expansion a = 0.f (1)f(2)f(3) . . . rational for any value of n ?

The decimal expansion of a is defined as follows: If f(x) = d_1(x)d_2(x) \cdots d_{r(x)}(x) is the decimal expansion of f(x), then a = 0.1d_1(2)d_2(2) \cdots d_{r(2)}(2)d_1(3) . . . d_{r(3)}(3)d_1(4) \cdots .

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