As the title says, I wonder whether there are sequences that can only be specified by recursion. In other words, are there any sequences $a_k$ where there is no other way to calculate $a_n$ than calculating $a_0$, $a_1$, ..., $a_{n-1}$ before? If so, can this be proven?
2026-04-02 11:09:50.1775128190
Sequences that can only be specified by recursion
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Let $a_n$ be the least prime greater than $a_{n-1}^2$ $\;(n=1,2,...$ ), with $a_0=2$.