Erdős problem 867 · problems.science

Is it true that if $A=\{a_1<\cdots <a_t\}\subseteq \{1,\ldots,N\}$ has no solutions to $a_i+a_{i+1}+\cdots+a_j\in A$ then $\lvert A\rvert \leq \frac{N}{2}+O(1)?$

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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

867.lean

Retained formal statement4 of 6

The current best bounds are due to Coppersmith and Phillips [CoPh96], who prove that the maximal size of such an $A$ satisfies $\lvert A\rvert \leq \left(\frac{2}{3}-\frac{1}{512}\right)N+\log N.$

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.coppersmith_phillips_upper_bound2 linesExact file

1∀ᶠ (N : ℕ) in Filter.atTop,2  ∀ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A → ↑A.card ≤ (2 / 3 - 1 / 512) * ↑N + Real.log ↑N

SolvedStatement only, no proof

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