A070136 Numbers m such that [A070080(m), A070081(m), A070082(m)] is a right integer triangle.

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

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,changed

Author

Reinhard Zumkeller, May 05 2002

Status

approved