Erdős problem 357 · problems.science

Let $f(n)$ be the maximal $k$ such that there exist integers $1 \le a_1 < \dotsc < a_k \le n$ such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. It is known that $f(n) \geq (2+o(1))\sqrt{n}$ . Source: See comment by Desmond Weisenberg here: https://www.erdosproblems.com/forum/thread/357.

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17 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

357.lean

Retained formal statement10 of 17

Suppose $A$ is an infinite set such that all finite sums of consecutive terms of $A$ are distinct. Then it is conjectured that the sum $\sum_k \frac{1}{a_k}$ converges.

FormalConjectures/ErdosProblems/357.leanErdos357.erdos_357.variants.infinite_set_sum1 lineExact file

1∀ (A : ℕ → ℕ), StrictMono A → Erdos357.HasDistinctSums A → Summable fun i => 1 / ↑(A i)

OpenStatement only, no proof

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