A376608 -id:A376608 - cp's OEIS frontend

A103605 Pythagorean triples in increasing order of perimeter (a+b+c). If two successive perimeters are equals, then in order of decreasing areas; each triple [a(i), a(j), a(k)] (with k multiple of 3, j=k-1, i=k-2) in increasing order.

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

Offset: 1

Alexandre Wajnberg, Mar 24 2005

The corresponding perimeters A009096. - Wolfdieter Lang, Oct 06 2014

Andreas Boe, Table of n, a(n) for n = 1..30000
Ron Knott, The Pythagorean triples.

For primitive triples see A103606.

Cf. A009096, A376608.

In the name second 'increasing' -> 'decreasing' (observed by A. Boe). - Wolfdieter Lang, Oct 06 2014

A374597 a(n) = floor(area) for the area of the largest square that can be inscribed in the n-th Pythagorean triangle, with one side of the square on the hypotenuse of the triangle, for Pythagorean triangles ordered first by increasing perimeter, then by shorter leg.

Original entry on oeis.org

2, 10, 11, 23, 24, 42, 28, 46, 65, 93, 94, 99, 75, 128, 52, 104, 168, 213, 112, 185, 223, 262, 269, 84, 318, 373, 156, 378, 290, 391, 444, 398, 252, 301, 515, 584, 209, 417, 591, 124, 673, 555, 621, 759, 632, 568, 839, 852, 269, 448, 949, 1038, 172, 742, 895, 1051, 679, 1077

Offset: 1

Alexander M. Domashenko, Jul 13 2024

nonn

For a triangle with leg lengths x,y, the square has side length x*y*z/(x*y + z^2) and the area rounded down is a(n) = f(x,y,z) = floor((x*y*z/(x*y + z^2))^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(3,4,5) = floor((3*4*5/(3*4+5^2))^2) = 2.

Alexander M. Domashenko, Problem 2176. Two squares in a triangle (in Russian).

Cf. A376608.

cp's OEIS Frontend

A103605 Pythagorean triples in increasing order of perimeter (a+b+c). If two successive perimeters are equals, then in order of decreasing areas; each triple [a(i), a(j), a(k)] (with k multiple of 3, j=k-1, i=k-2) in increasing order.

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