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    $\begingroup$ This looks correct to me. $2+A_7^{\leq 2}=\{2,9,16\}$ and $3+A_7^{\leq 2}=\{3,10,17\}$. Since the range of $j$ in the question is shown to include $0$, then $0\in \mathbb{N}$. $\endgroup$ Commented 17 hours ago
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    $\begingroup$ I wonder why the answer was downvoted? $\endgroup$ Commented 16 hours ago