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A299016
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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.
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0
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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