Does there exist positive integers $a_{1}<a_{2}<\cdots<a_{100}$ such that for $2 \le k \le 100$, the greatest common divisor of $a_{k-1}$ and $a_{k}$ is greater than the greatest common divisor of $a_{k}$ and $a_{k+1}$?
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Tags: greatest common divisor, More Sequences
Does there exist positive integers $a_{1}<a_{2}<\cdots<a_{100}$ such that for $2 \le k \le 100$, the greatest common divisor of $a_{k-1}$ and $a_{k}$ is greater than the greatest common divisor of $a_{k}$ and $a_{k+1}$?