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Search: id:A061281
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| A061281 |
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Side of n-th equilateral triangle enclosing at least one point located at integer distances from the vertices. |
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+0
5
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (wasserma(AT)spawar.navy.mil), Jun 10 2002. See A089025.
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REFERENCES
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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.
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A072052, A072053, A072054, A089025, A067900.
Sequence in context: A117723 A157662 A095615 this_sequence A119684 A119742 A154063
Adjacent sequences: A061278 A061279 A061280 this_sequence A061282 A061283 A061284
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KEYWORD
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nonn,more
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), May 21 2001
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 10 2002
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