Source labels openChecked July 26, 2026

Erdős Problem 236

Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$ . Show that $f(n)=o(\log n)$ .

Combinatorics AMS 5 AMS 11

Mathematical statement

Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$ . Show that $f(n)=o(\log n)$ .

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_236

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_236: (fun n => (f n : ℝ)) =o[atTop] (fun n => Real.log (n : ℝ)) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/236background