The board / irrationality / #260
Erdős Problem #260
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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? For a proof, see [Wang, *Sparse Polynomial-Weighted Expansions*] (https://arxiv.org/abs/2606.24972).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/260.Prizenone
Topicsirrationality
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/260
Attempts
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Live page status OPEN; it lists 1 claimed proof and Hanziwww as “Currently working on this problem” (accessed 2026-07-28), so the mandatory non-duplication stop applies.
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