It is often said that $\pi$ contains any string of digits. But does the property "transcendental" imply "contains any string of digits?
2026-03-28 03:56:10.1774670170
Do transcendental numbers contain any string of digits?
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No. Consider the Liouville number $\sum_k{\frac{1}{10^{k!}}}$. It is transcendental but all of its digits are $0$ or $1$. As for $\pi$, it is unknown whether it contains any string of digits, but it is conjectured to have the stronger property of being normal in all bases.