|
%I #10 Oct 11 2021 12:46:34
%S 5,8,13,14,20,21,25,26,29,30,32,36,37,41,42,44,49,50,52,56,57,59,61,
%T 62,66,67,69,74,75,77,78,79,80,82,86,87,89,91,96,97,99,100,101,102,
%U 104,105,110,111,113,115,118,122,123,125,126,127
%N Numbers n such that [A070080(n), A070081(n), A070082(n)] is an obtuse integer triangle.
%H Jean-François Alcover, <a href="/A070127/b070127.txt">Table of n, a(n) for n = 1..724</a>
%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%e 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.
%t m = 55 (* max perimeter *);
%t sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
%t triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]]&];
%t Position[triangles, {a_, b_, c_} /; a^2 + b^2 - c^2 < 0] // Flatten (* _Jean-François Alcover_, Oct 11 2021 *)
%Y Cf. A070101, A070129, A070130, A070131, A070132, A070133, A070134, A070135, A070128, A070085.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, May 05 2002
|
