MathDB

Let

{(a_n)_{n\ge1}}

be a sequence with

{a_1 = 1}

and

{a_{n+1} = \lfloor a_n +\sqrt{a_n}+\frac{1}{2}\rfloor }

for all

{n \ge 1}

, where

{\lfloor x \rfloor}

denotes the greatest integer less than or equal to

{x}

. Find all

{n \le 2013}

such that

{a_n}

is a perfect square

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