# Greedy Squares

Consider the following recursive process:

$a_{n+1}=a_n-\lfloor\sqrt{a_n}\rfloor^2$

For all positive integers $$a_0$$, the process above eventually results in $$a_n = 0$$ for all $$n \geq k$$ for some positive integer $$k$$. What is the first value of $$a_0$$ such that $$k=7\text{?}$$

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