%I
%S 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,
%T 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,
%U 1,8,8,7,5,2,1,2,3,4,5,6,6,5,4,2,1,5,10,10
%N 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(n1) such that the Zcoordinate of the cross product of the vectors (P(n1), P(n)) and (P(n1), P(j)) is strictly negative for j=1..n2, and in case of a tie, P(n) maximizes the dot product of the vectors (P(n2), P(n1)) and (P(n1), P(n)); a(n) = Xcoordinate of P(n).
%C More informally:
%C  the "scalar product" constraint means that the points P(1), ..., P(n2) are all on the left side of the fixed vector (P(n1), P(n)),
%C  the "dot product" constraint means the angle of the vectors (P(n2), P(n1)) and (P(n1), P(n)) is maximized.
%C See A292470 for the Ycoordinate of P(n).
%C 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.
%H Rémy Sigrist, <a href="/A292469/b292469.txt">Table of n, a(n) for n = 1..1000</a>
%H Rémy Sigrist, <a href="/A292469/a292469.png">Representation of the first hundred points of P, with consecutive points joined by a segment</a>
%H Rémy Sigrist, <a href="/A292469/a292469_1.png">Representation of the first 500 points of P, with consecutive points joined by a segment</a>
%H Rémy Sigrist, <a href="/A292469/a292469.txt">C++ program for A292469</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cross_product">Cross product</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dot_product">Dot product</a>
%e See representation of the first hundred points of P in Links section.
%o (C++) See Links section.
%Y Cf. A292470.
%K sign,look
%O 1,8
%A _Rémy Sigrist_, Sep 17 2017
