\(4\) has the property that if one adds it to double its square, it yields a perfect square. In other words for natural numbers \(m,n\):

\[n^2 + n^2 + n = m^2 \]

There are four such \(n<10^6 \). If \(4\) is the smallest \(n\), what is the second smallest \(n\)?

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