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A061281 Side of n-th equilateral triangle enclosing at least one point located at integer distances from the vertices. 6
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A340125 A095615 A361339 * A336329 A349206 A217149
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

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)