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A223941
Areas of primitive Heron triangles with two rational triangle medians.
2
420, 55440, 2042040, 23931600, 75698280, 142334216640, 1877686881840, 185643608470320, 2137147184560080
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
Cf. A181928.
A360537 is a subsequence.
Sequence in context: A135340 A135380 A035846 * A360537 A046167 A059951
KEYWORD
hard,more,nonn
AUTHOR
EXTENSIONS
a(7)-a(9) from Hone (2024) added by Andrey Zabolotskiy, Apr 06 2024
STATUS
approved