Median of a list and its squares

MediumCombinatorics Statistics~6m

Form the list $A = [\,1, 2, \dots, 2024,\ 1^2, 2^2, \dots, 2024^2\,]$ - that is, the integers $1$ through $2024$ together with their squares ( $4048$ numbers in all, with repeats kept). What is the median of $A$ ?

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With $4048$ numbers, the median averages the $2024$ th and $2025$ th smallest. Count entries $\le v$ .
That count is $v + \lfloor\sqrt v\rfloor$ . Solve it $= 2024$ to find where the median sits.

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Median of a list and its squares

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