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Erdős problem 32

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Does there exist a set A⊆NA \subseteq \mathbb{N} such that ∣A∩{1,…,N}∣=o((log⁡N)2)|A \cap \{1, \ldots, N\}| = o((\log N)^2) and every sufficiently large integer can be written as p+ap + a for some prime pp and a∈Aa \in A?

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5 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

32.lean

Retained formal statement1 of 5

Does there exist a set A⊆NA \subseteq \mathbb{N} such that ∣A∩{1,…,N}∣=o((log⁡N)2)|A \cap \{1, \ldots, N\}| = o((\log N)^2) and every sufficiently large integer can be written as p+ap + a for some prime pp and a∈Aa \in A?

FormalConjectures/ErdosProblems/32.leanErdos32.erdos_324 linesExact file
True ↔  ∃ A,    Erdos32.IsAdditiveComplementToPrimes A ∧      (fun N => ↑{x ∈ Finset.Icc 1 N | x ∈ A}.card) =o[Filter.atTop] fun N => Real.log ↑N ^ 2
OpenStatement only, no proof