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Solution :**

Suppose that the sequence {a_{n}} contains only
finitely many composite numbers. That means that there exists N such that for
all n > N a_{n} is odd.

Consider the
binary representation of a_{n}, n > N. The last digit of a_{n}
must be 1, which in turn implies that the fractional part of the binary
representation of has all its digits equal to 1 after N-th position. This
contradicts the irrationality of .