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Part of 2012 Miklós Schweitzer

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Miklós Schweitzer 2012 P1

Source: Miklós Schweitzer 2012 P1

8/20/2018
Is there any real number α\alpha for which there exist two functions f,g:N→Nf,g: \mathbb{N} \to \mathbb{N} such that α=lim⁡n→∞f(n)g(n),\alpha=\lim_{n \to \infty} \frac{f(n)}{g(n)}, but the function which associates to nn the nn-th decimal digit of α\alpha is not recursive?
recursivereal analysiscomputable analysiscollege contestsDiscrete Mathematics