A120133 - OEIS

%I #19 Nov 14 2019 19:35:29

%S 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,

%T 15,25,19,15,13,12,24,16,17,25,10,29,13,25,15,9,17,18,29,15,17,13,25,

%U 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

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

%H Giovanni Resta, <a href="/A120133/b120133.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/tritab.html">Heronian Triangle Table</a>

%H P. Yiu, <a href="http://math.fau.edu/yiu/RecreationalMathematics2003.pdf">Heron triangles with sides < 100</a>, Recreational Mathematics, Appendix Chap. 9.3 pp. 81/360. (This is a download of 360 pages.)

%t 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 *)

%Y Cf. A120131, A120132, A072294.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Jun 10 2006