A299016 Integer radii of circles over an integer lattice such that the number of unit squares whose centers are contained in the circle is less than the area of the circle.

2, 6, 12, 19, 24, 36, 40, 43, 48, 52, 53, 55, 60, 61, 65, 70, 74, 77, 89, 91, 108, 111, 116, 123, 125, 128, 129, 140, 141, 142, 146, 152, 154, 159, 166, 169, 171, 180, 181, 183, 184, 197, 198, 205, 209, 210, 212, 214, 222

Offset: 1

Author

Dimitri Papadopoulos, Jun 19 2018

Keywords

• nonn

Examples

			For the circle with radius a(1) = 2, the point  (3/2, 3/2 ), i.e. the center of the unit square bounded by x = 1, x = 2, y = 1, y = 2, is outside the circle of radius 2 centered at the origin so there are 12 unit squares with centers inside the circle of radius 2, and 12 <  Pi *2 *2.
		

Programs

Mathematica

t = {}; For[n = 1, n < 223, n++, cnt = 0; For[x = -n, x < 0, x++, For[y = -n, y < 0, y++, If[N[Norm[{x + 1/2, y + 1/2}]] < n, cnt++]]] If[Pi*n*n > 4*cnt, t = Append[t, n]]] Print[t];