A120132 - OEIS

%I #20 Nov 14 2019 19:34:46

%S 4,5,5,12,13,13,14,10,15,17,13,15,17,20,13,17,24,25,25,25,25,21,25,17,

%T 25,29,29,34,29,20,26,30,35,37,25,28,34,35,29,37,39,28,40,40,41,29,37,

%U 39,40,25,35,41,41,35,37,38,40,29,33,39,41,51,51,35,45,51,52,51,53,39

%N Middle side of primitive Heronian triangles, sorted on longest side (A120131), then on middle side.

%H Giovanni Resta, <a href="/A120132/b120132.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 < 300</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@ b], {a, 60}, {b, a}, {c, a-b+1, b}]][[2, 1]] (* _Giovanni Resta_, May 21 2016 *)

%Y Cf. A120131, A120133, A072294.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Jun 10 2006