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 A223941 Areas of primitive Heron triangles with two rational triangle medians. 1
 420, 55440, 2042040, 23931600, 75698280, 142334216640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are divisible by 30. 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. 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. Sequence in context: A135340 A135380 A035846 * A046167 A059951 A225992 Adjacent sequences:  A223938 A223939 A223940 * A223942 A223943 A223944 KEYWORD hard,more,nonn AUTHOR Arkadiusz Wesolowski, Mar 29 2013 STATUS approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)