If a circle is centered on the origin and has radius r, it may pass through some points with integer coordinates. In fact, by symmetry, this will be a multiple of 4.

Find the smallest radius that will pass through 4n integer points where n=1,2,3,4,5.

Feel free to go further.

**Sloane: A018782 **

**Smallest k such that circle x^2 + y^2 = k passes through exactly 4n integer points. **

`1, 5, 25, 65, 625, 325, 15625, 1105, 4225, 8125, 9765625, 5525, 244140625, 203125, 105625, 27625, 152587890625 etc`

*Edited on ***March 1, 2011, 11:25 am**