Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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