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Erdős problem 329

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Erdős Problem 329. Let A ⊆ ℕ be a Sidon set. How large can lim sup_{N → ∞} |A ∩ {1,…,N}| / N^{1/2} be?

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FormalConjectures/ErdosProblems/

329.lean

Retained formal statement3 of 6

Krückeberg ([Kr61]) exhibited an infinite Sidon set A with sidonUpperDensity A = 1 / Real.sqrt 2, improving Erdős’ earlier 1 / 2 lower bound.

[Kr61] Krückeberg, Fritz, Unparsed notation: B\sb{2}-Folgen und verwandte Zahlenfolgen. J. Reine Angew. Math. (1961), 53-60.

FormalConjectures/ErdosProblems/329.leanErdos329.erdos_329.variants.kruckeberg_19611 lineExact file
∃ A, IsSidon A ∧ Erdos329.sidonUpperDensity A = 1 / √2
SolvedStatement only, no proof