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Erdős problem 359

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Suppose monotone sequence AA satisfies the following: A 0 = 1 and for all j, A (j + 1) is the smallest natural number that cannot be written as a sum of consecutive terms of A 0, ..., A j. Then it is conjectured that ak klog⁡klog⁡log⁡ka_k ~ \frac{k \log k}{\log \log k}.

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FormalConjectures/ErdosProblems/

359.lean

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Suppose monotone sequence AA satisfies the following: A 0 = 1 and for all j, A (j + 1) is the smallest natural number that cannot be written as a sum of consecutive terms of A 0, ..., A j. Then it is conjectured that ak klog⁡klog⁡log⁡ka_k ~ \frac{k \log k}{\log \log k}.

FormalConjectures/ErdosProblems/359.leanErdos359.erdos_359.variants.isGoodFor_1_asymptotic3 linesExact file
∀ (A : ℕ → ℕ),  Erdos359.IsGoodFor A 1 →    Asymptotics.IsEquivalent Filter.atTop (fun k => ↑(A k)) fun k => ↑k * Real.log ↑k / Real.log (Real.log ↑k)
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