I was just doing some complex sequences and I came across this: $$\frac{1\pm i\sqrt 3}{2}, 1\pm i, \frac{3\pm i\sqrt 3}{2}, 2, \frac{5\pm\sqrt 5}{2}, 3\pm\sqrt 3, \frac{7\pm\sqrt {21}}{2}, 4\pm 2\sqrt 2, \frac{9\pm 3\sqrt 5}{2}, 5\pm\sqrt 15, \frac{11\pm\sqrt{77}}{2}\cdots$$
And I couldn’t find any pattern and I don’t know how to find an explicit formula for this, if you need, I can list down more terms. Please help me. And yes, there is no $i$ after the third term.
The $n^\text{th}$ term is the roots of the quadratic $x^2-nx+n=0$.