login
Sides x < y < z of Pythagorean triangles ordered first by increasing perimeter x+y+z, then by shorter leg x.
2

%I #10 Oct 05 2024 14:34:18

%S 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,

%T 25,20,21,29,18,24,30,16,30,34,12,35,37,21,28,35,9,40,41,15,36,39,24,

%U 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

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

%e Triangle

%e | Perimeter

%e | x y z

%e 1 12 [ 3, 4, 5]

%e 2 24 [ 6, 8, 10]

%e 3 30 [ 5, 12, 13]

%e 4 36 [ 9, 12, 15]

%e 5 40 [ 8, 15, 17]

%e 6 48 [12, 16, 20]

%e 7 56 [ 7, 24, 25]

%e 8 60 [10, 24, 26]

%e 9 60 [15, 20, 25]

%e 10 70 [20, 21, 29]

%Y Cf. A010814, A024364, A103605.

%Y A374597 uses this order of sides.

%K nonn,tabf

%O 1,1

%A _Hugo Pfoertner_, Sep 29 2024