Erdős problem 264 · problems.science

Kovač and Tao [KoTa24] generally proved that any strictly increasing sequence of positive integers $a_n$ such that $\sum \frac{1}{a_n}$ converges and $\liminf_{n \to \infty} (a_n^2 \sum_{k > n} \frac{1}{a_k^2}) > 0$ is not an irrationality sequence.

Sources

Browse retained paths and inspect the exact material available for this Problem.

5 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

264.lean

Retained formal statement1 of 5

Is $2^n$ an example of an irrationality sequence? Kovač and Tao proved that it is not [KoTa24]

[KoTa24] Kovač, V. and Tao T., On several irrationality problems for Ahmes series. arXiv:2406.17593 (2024).

FormalConjectures/ErdosProblems/264.leanErdos264.erdos_264.parts.i1 lineExact file

1¬Erdos264.IsIrrationalitySequence fun x => 2 ^ x

SolvedStatement only, no proofformal statement reference

Sources

Search problems.science