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A308982
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Areas of integer rectangles circumscribed by increasingly large circles.
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0
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1, 2, 4, 3, 6, 4, 9, 8, 12, 5, 10, 16, 15, 6, 12, 20, 18, 7, 25, 24, 14, 21, 30, 8, 28, 16, 36, 24, 35, 32, 9, 18, 42, 40, 27, 36, 49, 48, 10, 20, 45, 30, 56, 40, 54, 11, 22, 50, 64, 33, 63, 60, 44, 12, 72, 55, 24, 70, 36, 66, 48, 81, 80, 60, 13, 77, 26, 39
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OFFSET
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1,2
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COMMENTS
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Sort all rectangles with integer side lengths by the radius of the circle that circumscribes them. Ties are broken by sorting by area. The terms of the sequence are the areas of the rectangles.
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LINKS
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EXAMPLE
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a(1) is a 1 X 1 rectangle; r = sqrt(1^2 + 1^2) = sqrt(2); A = 1.
a(2) is a 2 X 1 rectangle; r = sqrt(2^2 + 1^2) = sqrt(5); A = 2.
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MATHEMATICA
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Times @@@ Take[Flatten[ SortBy[#, Times @@ # &] & /@ GatherBy[ SortBy[ Union[Sort /@ Tuples[ Range[70], 2]], Total[#^2] &], Total[#^2] &], 1], 70] (* Giovanni Resta, Jul 18 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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