cp's OEIS Frontend

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.

%I A299016 #23 Jan 30 2019 06:13:09
%S A299016 2,6,12,19,24,36,40,43,48,52,53,55,60,61,65,70,74,77,89,91,108,111,
%T A299016 116,123,125,128,129,140,141,142,146,152,154,159,166,169,171,180,181,
%U A299016 183,184,197,198,205,209,210,212,214,222
%N 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.
%e A299016 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 A299016 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 A299016 nonn
%O A299016 1,1
%A A299016 _Dimitri Papadopoulos_, Jun 19 2018