MathDB

Determine the maximal length

L

of a sequence

a_1,\dots,a_L

of positive integers satisfying both the following properties:
[*]every term in the sequence is less than or equal to

2^{2023}

, and [*]there does not exist a consecutive subsequence

a_i,a_{i+1},\dots,a_j

(where

1\le i\le j\le L

) with a choice of signs

s_i,s_{i+1},\dots,s_j\in\{1,-1\}

for which

s_ia_i+s_{i+1}a_{i+1}+\dots+s_ja_j=0.

Problem Statement