We prove, that $$ \biggl\|\biggl(\frac43\biggr)^k\biggr\| >\biggl(\frac49\biggr)^k\qquad\text{for}\quad k\ge6, $$ where $\|\cdot\|$ is a distance to the nearest prime.
A lower bound for periods of matrices
On the lower bound of the discrepancy of (t; s) sequences: I
On the lower bound of the discrepancy of $(t,s)$ sequences: II
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