Let $k>2$. Can we determine $\displaystyle \max_{m\in\mathbb N}\frac1{k10^{m!}}-\frac2{10^{(m+1)!}}$ ? Or at least a non trivial lower bound of this maximum?
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Is there a link with the famous constant $0.123456789...$ – Miss and Mister cassoulet char Mar 16 '23 at 09:51
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It could be much easier to consider the continuous problem – Claude Leibovici Mar 16 '23 at 10:25