A374597 -id:A374597 - cp's OEIS frontend

A376608 Sides x < y < z of Pythagorean triangles ordered first by increasing perimeter x+y+z, then by shorter leg x.

3, 4, 5, 6, 8, 10, 5, 12, 13, 9, 12, 15, 8, 15, 17, 12, 16, 20, 7, 24, 25, 10, 24, 26, 15, 20, 25, 20, 21, 29, 18, 24, 30, 16, 30, 34, 12, 35, 37, 21, 28, 35, 9, 40, 41, 15, 36, 39, 24, 32, 40, 27, 36, 45, 14, 48, 50, 20, 48, 52, 24, 45, 51, 30, 40, 50, 28, 45, 53, 11, 60, 61, 33, 44, 55

Offset: 1

Hugo Pfoertner, Sep 29 2024

			   Triangle
   |  Perimeter
   |       x   y   z
   1  12 [ 3,  4,  5]
   2  24 [ 6,  8, 10]
   3  30 [ 5, 12, 13]
   4  36 [ 9, 12, 15]
   5  40 [ 8, 15, 17]
   6  48 [12, 16, 20]
   7  56 [ 7, 24, 25]
   8  60 [10, 24, 26]
   9  60 [15, 20, 25]
  10  70 [20, 21, 29]

Cf. A010814, A024364, A103605.

A374597 uses this order of sides.

A374596 Floor(area) for the area of the largest square which fits in each Pythagorean triangle, with sides of the square on the legs of the triangle, for Pythagorean triangles ordered first by increasing perimeter, then shorter leg, then longer leg.

Original entry on oeis.org

2, 11, 12, 26, 27, 47, 29, 49, 73, 104, 105, 108, 79, 144, 53, 112, 188, 238, 117, 199, 244, 293, 297, 86, 355, 419, 162, 423, 311, 431, 496, 435, 264, 319, 576, 656, 215, 448, 661, 126, 752, 601, 680, 849, 687, 610, 944, 952, 276, 469, 1060, 1166, 174, 797, 979

Offset: 1

Alexander M. Domashenko, Jul 13 2024

nonn

For a triangle with leg lengths x,y, the square has side length x*y/(x+y) and the area rounded down is a(n) = f(x,y) = floor( (x*y/(x+y))^2 ).

			The first Pythagorean triangle is (x,y,z) = (3,4,5) and the rounded area of the square inside it is a(1) = f(3,4) = floor((3*4/(3+4))^2) = 2.

Cf. A374597.

cp's OEIS Frontend

A376608 Sides x < y < z of Pythagorean triangles ordered first by increasing perimeter x+y+z, then by shorter leg x.

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