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A308982 Areas of integer rectangles circumscribed by increasingly large circles. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
Times @@@ Take[Flatten[ SortBy[#, Times @@ # &] & /@ GatherBy[ SortBy[ Union[Sort /@ Tuples[ Range[70], 2]], Total[#^2] &], Total[#^2] &], 1], 70] (* Giovanni Resta, Jul 18 2019 *)
CROSSREFS
Cf. A024509.
Sequence in context: A151734 A175027 A269837 * A182298 A182732 A119477
KEYWORD
nonn
AUTHOR
Dave Rutt, Jul 04 2019
EXTENSIONS
More terms from Giovanni Resta, Jul 17 2019
STATUS
approved

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Last modified July 13 20:42 EDT 2024. Contains 374288 sequences. (Running on oeis4.)