 There is no question that \(\ba\) is a computationally well-defined sequence, in the sense that we have an algorithm for computing \(a_n\) for each \(n\): check the even numbers \(4,6,8,\ldots ,2n+2\) to determine whether each of them is a sum of two primes; in that case, set \(a_n = 0\), and in the contrary case, set \(a_n = 1\). Now consider the real number whose \(n\)th binary digit is \(a_n\):