A070111 Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with prime sides.

3, 5, 6, 9, 14, 16, 22, 30, 34, 35, 43, 46, 63, 84, 101, 109, 124, 133, 153, 159, 163, 170, 189, 193, 201, 234, 240, 286, 297, 328, 334, 350, 352, 382, 392, 410, 444, 450, 454, 472, 478, 479, 515, 519, 527, 542, 544, 597, 603, 621, 629, 688, 708, 714, 771, 777, 795, 799, 811, 817, 868, 878, 900, 907, 911

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Examples

			35 is a term: [A070080(35), A070081(35), A070082(35)]=[2,7,7].
		

Links

• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

Cf. A070088, A070114, A070117, A070120, A070123, A070126, A070129, A070132, A070135.

Programs

Mathematica

m = 50 (* 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_} /; AllTrue[{a, b, c}, PrimeQ]] // Flatten (* Jean-François Alcover, Oct 04 2021 *)

Extensions

More terms from Jean-François Alcover, Oct 04 2021