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All Random Solved Random Open
OPEN
Let $n_1<n_2<\cdots$ be a sequence of integers such that \[\limsup \frac{n_k}{k}=\infty.\] Is \[\sum_{k=1}^\infty \frac{1}{2^{n_k}}\] transcendental?
Erdős [Er75c] proved the answer is yes under the stronger condition that $\limsup n_k/k^t=\infty$ for all $t\geq 1$.