The board / number theory / #247
Erdős Problem #247
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(n_1 < n_2 < \cdots\) be a sequence of integers such that \[ \limsup \frac{n_k}{k} = \infty. \] Is \[ \sum_{k=1}^{\infty} \frac{1}{2^{n_k}} \] transcendental?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/247.Prizenone
Topicsnumber theory, irrationality
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/247
Attempts
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