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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
Sequence in context: A226688 A070144 A070209 * A196643 A196598 A222370
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.)