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 A070136 Numbers m such that [A070080(m), A070081(m), A070082(m)] is a right integer triangle. 6
 17, 116, 212, 370, 493, 850, 1297, 1599, 1629, 2574, 2778, 3751, 4298, 4370, 5251, 5286, 6476, 9169, 10066, 12398, 12441, 12520, 14414, 16365, 16602, 19831, 21231, 21486, 24060, 26125, 27245, 29230, 33625, 33658 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Right integer triangles have integer areas: see A070142. LINKS Jean-François Alcover, Table of n, a(n) for n = 1..137 Eric Weisstein's World of Mathematics, Heronian Triangle. Eric Weisstein's World of Mathematics, Right Triangle. Reinhard Zumkeller, Integer-sided triangles EXAMPLE 116 is a term: [A070080(116), A070081(116), A070082(116)]=[6,8,10], A070085(116)=6^2+8^2-10^2=36+64-100=0. 212 is a term: [A070080(212), A070081(212), A070082(212)]=[5,12,13], A070085(212)=5^2+12^2-13^2=25+144-169=0. MATHEMATICA m = 500 (* max perimeter *); sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &]; triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &]; Position[triangles, {a_, b_, c_} /; a^2 + b^2 == c^2] // Flatten (* Jean-François Alcover, Oct 12 2021 *) CROSSREFS Cf. A024155, A070137, A070142, A070085. Sequence in context: A226688 A070144 A070209 * A196643 A196598 A222370 Adjacent sequences: A070133 A070134 A070135 * A070137 A070138 A070139 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified May 20 06:19 EDT 2024. Contains 372703 sequences. (Running on oeis4.)