MathDB

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 .

Problem Statement