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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

Table of n, a(n) for n=1..6.

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.)