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Oct 23, 2023 at 8:01 comment added Fedor Petrov I would try a random $N$-periodic sequence with probability of $j$ proportional to $1/j$, and try to apply some version of Lovász local lemma.
Oct 22, 2023 at 18:44 comment added Roland Bacher This shows $B(\lambda)>\lambda$. My computer suggests that perhaps $\lim_{\lambda\rightarrow\infty}B(\lambda)/\lambda=1$. (I got $B(500)\leq 519$.)
Oct 22, 2023 at 18:09 vote accept Roland Bacher
Oct 22, 2023 at 13:24 history answered Fedor Petrov CC BY-SA 4.0