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

1,1

Links

Jean-François Alcover, Table of n, a(n) for n = 1..1778

Reinhard Zumkeller, Integer-sided triangles

Example

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.

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 *)

Crossrefs

Cf. A070097, A070118, A070111, A070112.

Sequence in context: A154378 A300145 A063372 * A119659 A263161 A268772

Adjacent sequences: A070120 A070121 A070122 * A070124 A070125 A070126

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved