turing machine decidability proof
Can you come up with a Turing machine that writes the decimal expansion of $\pi$ to tape?
Can you come up with a Turing machine that, given a string,
a separator, and the decimal expansion of $\pi$ on the tape,
determines whether the string occurs as a subsequence of $\pi$? (see this question).
Given such machines, can you 'weave' them into a single machine?