Erdős problem 260 · problems.science

Let $a_1 < a_2 < \cdots$ be an increasing sequence such that $\frac{a_n}{n} \to \infty$ . Is the sum $\sum_{n}^{\infty} \frac{a_n}{2^{a_n}}$ irrational?

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FormalConjectures/ErdosProblems/

260.lean

Retained formal statement1 of 1

Let $a_1 < a_2 < \cdots$ be an increasing sequence such that $\frac{a_n}{n} \to \infty$ . Is the sum $\sum_{n}^{\infty} \frac{a_n}{2^{a_n}}$ irrational?

FormalConjectures/ErdosProblems/260.leanErdos260.erdos_2605 linesExact file

1sorry ↔2  ∀ (a : ℕ → ℤ) (s : ℝ),3    StrictMono a →4      Filter.Tendsto (fun n => ↑(a n) / ↑n) Filter.atTop Filter.atTop →5        HasSum (fun n => ↑(a n) / 2 ^ a n) s → Irrational s

OpenStatement only, no proof

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