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Side of n-th equilateral triangle enclosing at least one point located at integer distances from the vertices.
6

%I #17 Jul 07 2023 14:52:51

%S 112,147,185,224,273,283,294,331,331,336,370,403,441,448,485,520,546,

%T 555,559,560,566,588,592,637,645,662,662,672,691,735,740,784,806,819,

%U 849,882,896,925,965,970,993,993,1008,1029,1040,1047,1092,1110,1118,1120,1132

%N Side of n-th equilateral triangle enclosing at least one point located at integer distances from the vertices.

%C The equation has many other integer solutions, such as {3,5,7,8}; most of these describe points that lie on the edge of the triangle. - _David Wasserman_, Jun 10 2002. See A089025.

%D M. Gardner, Mathematical Circus, Alfred A. Knopf, 1979, p. 65.

%D L. Pianaro, Pierre Est Encore Perdu, Jouer Jeux Mathematiques, No. 18, Oct 1995, published by French Federation of Mathematics Games.

%F a(n) is the largest term in the n-th quadruple (a, b, c, d) satisfying the triangle equation 3*(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.

%e The solution (97,185,208,273) of the triangle equation gives rise to the value 273 as the 5th equilateral triangle associated with an interior point at integer distances from the vertices.

%Y Cf. A072052, A072053, A072054, A089025.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, May 21 2001

%E More terms from _David Wasserman_, Jun 10 2002

%E More terms from _Jinyuan Wang_, Jul 20 2020