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Jun 25, 2023 at 15:11 comment added was_n Thanks for your comment @TerryTao. This perfectly solves my question.
Jun 24, 2023 at 18:46 comment added Terry Tao It seems that this is solved by $a_i = p^i (1-2p)^{n-i} \binom{n}{i}$ by a rearrangement of the binomial formula $(1-p)^{n-i} = \sum_{k=0}^{n-i} \binom{n-i}{k} p^k (1-2p)^{n-i-k}$, so yes once $p \leq 1/2$.
Jun 24, 2023 at 16:06 history edited was_n CC BY-SA 4.0
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Jul 9, 2023 at 3:05
Jun 24, 2023 at 15:05 history edited was_n CC BY-SA 4.0
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S Jun 24, 2023 at 15:05 review First questions
Jun 24, 2023 at 15:06
S Jun 24, 2023 at 15:05 history asked was_n CC BY-SA 4.0