A070127 Numbers n such that [A070080(n), A070081(n), A070082(n)] is an obtuse integer triangle.

5, 8, 13, 14, 20, 21, 25, 26, 29, 30, 32, 36, 37, 41, 42, 44, 49, 50, 52, 56, 57, 59, 61, 62, 66, 67, 69, 74, 75, 77, 78, 79, 80, 82, 86, 87, 89, 91, 96, 97, 99, 100, 101, 102, 104, 105, 110, 111, 113, 115, 118, 122, 123, 125, 126, 127

Offset

1,1

Links

Jean-François Alcover, Table of n, a(n) for n = 1..724

R. Zumkeller, Integer-sided triangles

Example

a(10)=30: [A070080(30), A070081(30), A070082(30)]=[3,5,7], A070085(30)=3^2+5^2-7^2=9+25-49=-15<0.

Mathematica

m = 55 (* 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 < 0] // Flatten (* Jean-François Alcover, Oct 11 2021 *)

Crossrefs

Cf. A070101, A070129, A070130, A070131, A070132, A070133, A070134, A070135, A070128, A070085.

Sequence in context: A078412 A144650 A046038 * A070128 A263263 A314420

Adjacent sequences: A070124 A070125 A070126 * A070128 A070129 A070130

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved