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%I #12 Oct 12 2021 21:57:18
%S 240,544,799,911,1262,1568,2621,2681,2856,3369,3648,4246,5194,5541,
%T 6576,6626,6725,7441,7503,7565,7902,7944,8882,8956,9332,9452,9472,
%U 9888,9988,10421,10498,10502,11075,11079,11622
%N Numbers m such that [A070080(m), A070081(m), A070082(m)] is an acute scalene integer triangle with prime side lengths.
%H Jean-François Alcover, <a href="/A070123/b070123.txt">Table of n, a(n) for n = 1..1778</a>
%H Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%e 240 is a term because: [A070080(240), A070081(240), A070082(240)]=[7<11<13], A070085(240)=7^2+11^2-13^2=49+121-169=1>0.
%t m = 500 (* 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 < b < c && AllTrue[{a, b, c}, PrimeQ] && a^2 + b^2 - c^2 > 0] // Flatten (* _Jean-François Alcover_, Oct 12 2021 *)
%Y Cf. A070097, A070118, A070111, A070112.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, May 05 2002
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