OFFSET
1,1
COMMENTS
All terms are divisible by 30.
It is not certain whether other values lie between those given. - Peter Luschny and Andrey Zabolotskiy, Apr 08 2024
LINKS
Ralph H. Buchholz and Randall L. Rathbun, An infinite set of Heron triangles with two rational medians, The American Mathematical Monthly, Vol. 104, No. 2 (Feb., 1997), pp. 107-115.
Andrew N. W. Hone, Heron Triangles and the Hunt for Unicorns, Math. Intelligencer (2024); arXiv:2401.05581 [math.NT], 2024.
Eric Weisstein's World of Mathematics, Heronian Triangle
MATHEMATICA
(*Brute-force search*)lst = {}; Do[s = (a + b + c)/2; d = Sqrt[s*(s - a)*(s - b)*(s - c)]; If[IntegerQ[d] && Divisible[d, 30] && d > 0, p = {{a, c, b}, {b, c, a}}; t = 0; Do[m = 1/2*Sqrt[2*p[[n, 1]]^2 + 2*p[[n, 2]]^2 - p[[n, 3]]^2]; If[MatchQ[m, _Rational] || IntegerQ[m], t++, Break[]], {n, 2}]; If[t == 2, AppendTo[lst, d]]], {a, 73}, {b, 51}, {c, 26}]; lst
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Arkadiusz Wesolowski, Mar 29 2013
EXTENSIONS
a(7)-a(9) from Hone (2024) added by Andrey Zabolotskiy, Apr 06 2024
STATUS
approved