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Erdős problem 247

Let n1<n2<⋯n_1 < n_2 < \cdots be a sequence of integers such that lim sup⁡nkk=∞. \limsup \frac{n_k}{k} = \infty. Is ∑k=1∞12nk \sum_{k=1}^{\infty} \frac{1}{2^{n_k}} transcendental?

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FormalConjectures/ErdosProblems/247.lean

Formal Conjectures

FormalConjectures/ErdosProblems/247.leanErdos247.erdos_2474 linesExact file
True ↔  ∀ (n : ℕ → ℕ),    StrictMono n →      Filter.limsup (fun k => ↑(n k) / ↑k.succ) Filter.atTop = ⊤ → Transcendental ℚ (∑' (k : ℕ), 1 / 2 ^ n k)
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