A308982 Areas of integer rectangles circumscribed by increasingly large circles.

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

Offset: 1

Author

Dave Rutt, Jul 04 2019

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A024509.

Programs

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 *)

Extensions

More terms from Giovanni Resta, Jul 17 2019