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Erdős problem 867

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Is it true that if A={a1<⋯<at}⊆{1,…,N}A=\{a_1<\cdots <a_t\}\subseteq \{1,\ldots,N\} has no solutions to ai+ai+1+⋯+aj∈Aa_i+a_{i+1}+\cdots+a_j\in A then ∣A∣≤N2+O(1)?\lvert A\rvert \leq \frac{N}{2}+O(1)?

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6 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

867.lean

Retained formal statement5 of 6

Freud [Fr93] constructed a sequence with density ≥19/36\geq 19/36.

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.freud2 linesExact file
∀ (ε : ℝ),  0 < ε → ∀ᶠ (N : ℕ) in Filter.atTop, ∃ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A ∧ (19 / 36 - ε) * ↑N ≤ ↑A.card
SolvedStatement only, no proof