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 A070142 Numbers n such that [A070080(n), A070081(n), A070082(n)] is an integer triangle with integer area. 11
 17, 39, 52, 116, 212, 252, 269, 368, 370, 372, 375, 493, 561, 587, 659, 839, 850, 862, 957, 972, 1156, 1186, 1196, 1204, 1297, 1582, 1599, 1629, 1912, 1920, 1955, 1971, 1988, 2115, 2352, 2555, 2574, 2713, 2774, 2778, 2790 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. Zumkeller, Integer-sided triangles Eric Weisstein's World of Mathematics, Heronian Triangle. EXAMPLE a(2)=39: [A070080(39), A070081(39), A070082(39)] = [5,5,6], area^2 = s*(s-5)*(s-5)*(s-6) with s=A070083(39)/2=(5+5+6)/2=8, area^2=8*3*3*2=16*9 is an integer square, therefore A070086(39)=area=4*3=12. MATHEMATICA maxPerim = 100; maxSide = Floor[(maxPerim - 1)/2]; order[{a_, b_, c_}] := (a + b + c)*maxPerim^3 + a*maxPerim^2 + b*maxPerim + c; triangles = Reap[ Do[ If[ a + b + c <= maxPerim && c - b < a < c + b && b - a < c < b + a && c - a < b < c + a, Sow[{a, b, c}]], {a, 1, maxSide}, {b, a, maxSide}, {c, b, maxSide}]][[2, 1]]; stri = Sort[ triangles, order[#1] < order[#2]&]; area[{a_, b_, c_}] := With[{p = (a + b + c)/2}, Sqrt[p*(p - a)*(p - b)*(p - c)]]; Position[ stri, tri_ /; IntegerQ[area[tri]]] // Flatten (* Jean-François Alcover, Feb 22 2013 *) CROSSREFS Cf. A070088, A070149, A070143, A070144, A070145, A051516, A069594, A069597, A070136, A070137, A070209. Sequence in context: A259489 A226127 A156777 * A070143 A274555 A140679 Adjacent sequences:  A070139 A070140 A070141 * A070143 A070144 A070145 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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