A061281 Side of n-th equilateral triangle enclosing at least one point located at integer distances from the vertices.

112, 147, 185, 224, 273, 283, 294, 331, 331, 336, 370, 403, 441, 448, 485, 520, 546, 555, 559, 560, 566, 588, 592, 637, 645, 662, 662, 672, 691, 735, 740, 784, 806, 819, 849, 882, 896, 925, 965, 970, 993, 993, 1008, 1029, 1040, 1047, 1092, 1110, 1118, 1120, 1132

Offset: 1

Author

Lekraj Beedassy, May 21 2001

Keywords

• nonn

Comments

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.

Examples

			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.
		

References

• M. Gardner, Mathematical Circus, Alfred A. Knopf, 1979, p. 65.
• L. Pianaro, Pierre Est Encore Perdu, Jouer Jeux Mathematiques, No. 18, Oct 1995, published by French Federation of Mathematics Games.

Crossrefs

Cf. A072052, A072053, A072054, A089025.

Formula

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.

Extensions

More terms from David Wasserman, Jun 10 2002

More terms from Jinyuan Wang, Jul 20 2020