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 statement15 of 17

Let $h(n)$ be the maximal $k$ such that there exist integers $1 \le a_1 \leq \dotsc \leq a_k \le n$ such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. How does $h(n)$ grow? Can we find a (good) explicit function $g$ such that $g = o(h)$ ?

FormalConjectures/ErdosProblems/357.leanErdos357.erdos_357.variants.monotone.parts.ii.littleO_version1 lineExact file

1sorry =o[Filter.atTop] fun n => ↑(Erdos357.h n)

OpenStatement only, no proof

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