A070123 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an acute scalene integer triangle with prime side lengths.

240, 544, 799, 911, 1262, 1568, 2621, 2681, 2856, 3369, 3648, 4246, 5194, 5541, 6576, 6626, 6725, 7441, 7503, 7565, 7902, 7944, 8882, 8956, 9332, 9452, 9472, 9888, 9988, 10421, 10498, 10502, 11075, 11079, 11622

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Examples

			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.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1778
• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

Cf. A070097, A070118, A070111, A070112.

Programs

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 < b < c && AllTrue[{a, b, c}, PrimeQ] && a^2 + b^2 - c^2 > 0] // Flatten (* Jean-François Alcover, Oct 12 2021 *)