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%I #23 Jan 30 2019 06:13:09
%S 2,6,12,19,24,36,40,43,48,52,53,55,60,61,65,70,74,77,89,91,108,111,
%T 116,123,125,128,129,140,141,142,146,152,154,159,166,169,171,180,181,
%U 183,184,197,198,205,209,210,212,214,222
%N 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.
%e 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.
%t 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];
%K nonn
%O 1,1
%A _Dimitri Papadopoulos_, Jun 19 2018
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