Erdős problem 263 · problems.science

Must every irrationality sequence $a_n$ in the above sense satisfy $a_n^{1/n} \to \infty$ as $n \to \infty$ ?

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6 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

263.lean

Retained formal statement4 of 6

A folklore result states that any $a_n$ satisfying $\lim_{n \to \infty} a_n^{\frac{1}{2^n}} = \infty$ has $\sum \frac{1}{a_n}$ converging to an irrational number.

FormalConjectures/ErdosProblems/263.leanErdos263.erdos_263.variants.folklore2 linesExact file

1∀ (a : ℕ → ℕ),2  Filter.Tendsto (fun n => ↑(a n) ^ (1 / 2 ^ n)) Filter.atTop Filter.atTop → Irrational (∑' (n : ℕ), 1 / ↑(a n))

SolvedStatement only, no proof

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