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

1,1

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.

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.

Links

Table of n, a(n) for n=1..51.

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.

Example

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.

Crossrefs

Cf. A072052, A072053, A072054, A089025.

Sequence in context: A340125 A095615 A361339 * A336329 A349206 A217149

Adjacent sequences: A061278 A061279 A061280 * A061282 A061283 A061284

Keyword

nonn

Author

Lekraj Beedassy, May 21 2001

Extensions

More terms from David Wasserman, Jun 10 2002

More terms from Jinyuan Wang, Jul 20 2020

Status

approved