A120133 Shortest side of primitive Heronian triangles, sorted on longest side(A120131), then on middle side(A120132) and finally on shortest side.

3, 5, 5, 5, 10, 4, 13, 9, 8, 16, 11, 7, 10, 13, 13, 12, 7, 14, 3, 17, 17, 20, 6, 17, 11, 5, 8, 15, 25, 19, 15, 13, 12, 24, 16, 17, 25, 10, 29, 13, 25, 15, 9, 17, 18, 29, 15, 17, 13, 25, 29, 21, 39, 26, 20, 25, 13, 27, 25, 37, 15, 5, 25, 24, 28, 4, 51, 26, 20, 25, 53, 33, 41, 17, 15, 11

Offset: 1

Author

Lekraj Beedassy, Jun 10 2006

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Michael Somos, Heronian Triangle Table
• P. Yiu, Heron triangles with sides < 100, Recreational Mathematics, Appendix Chap. 9.3 pp. 81/360. (This is a download of 360 pages.)

Crossrefs

Cf. A120131, A120132, A072294.

Programs

Mathematica

hQ[a_,b_,c_] := IntegerQ@ Sqrt@ Block[{s = (a+b+c)/2}, s (s-a) (s-b) (s-c)]; Reap[Do[If[ GCD[a, b, c] == 1 && hQ[a, b, c], Sow@c], {a, 60}, {b, a}, {c, a-b+1, b}]][[2, 1]] (* Giovanni Resta, May 21 2016 *)