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 A292469 Let P be the sequence of distinct lattice points defined by the following rules: P(1) = (0,0), P(2) = (1,0), and for any n > 2, P(n) is the closest lattice point to P(n-1) such that the Z-coordinate of the cross product of the vectors (P(n-1), P(n)) and (P(n-1), P(j)) is strictly negative for j=1..n-2, and in case of a tie, P(n) maximizes the dot product of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)); a(n) = X-coordinate of P(n). 3
 0, 1, 1, 0, -1, -1, 0, 2, 2, 1, 0, -1, -2, -2, -1, 1, 4, 4, 3, 2, -1, -2, -3, -3, -2, -1, 1, 4, 5, 5, 4, 2, 1, -1, -2, -3, -4, -4, -3, 0, 2, 5, 6, 6, 5, 3, 0, -1, -2, -3, -4, -5, -5, -4, -2, 1, 8, 8, 7, 5, 2, 1, -2, -3, -4, -5, -6, -6, -5, -4, -2, 1, 5, 10, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS More informally: - the "scalar product" constraint means that the points P(1), ..., P(n-2) are all on the left side of the fixed vector (P(n-1), P(n)), - the "dot product" constraint means the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)) is maximized. See A292470 for the Y-coordinate of P(n). The points of sequence P spin around the origin, and the segments joining consecutive points of P do not intersect (except at the common endpoint of two consecutive segments); these properties are the original motivations for this sequence. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..1000 Rémy Sigrist, C++ program for A292469 Wikipedia, Cross product Wikipedia, Dot product EXAMPLE See representation of the first hundred points of P in Links section. PROG (C++) See Links section. CROSSREFS Cf. A292470. Sequence in context: A293772 A293680 A293539 * A307011 A285007 A194527 Adjacent sequences:  A292466 A292467 A292468 * A292470 A292471 A292472 KEYWORD sign,look AUTHOR Rémy Sigrist, Sep 17 2017 STATUS approved

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Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)