cp's OEIS Frontend

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).

%I A292469 #22 Oct 27 2017 02:22:29
%S A292469 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 A292469 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 A292469 1,8,8,7,5,2,1,-2,-3,-4,-5,-6,-6,-5,-4,-2,1,5,10,10
%N 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).
%C A292469 More informally:
%C A292469 - 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)),
%C A292469 - the "dot product" constraint means the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)) is maximized.
%C A292469 See A292470 for the Y-coordinate of P(n).
%C A292469 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 A292469 Rémy Sigrist, <a href="/A292469/b292469.txt">Table of n, a(n) for n = 1..1000</a>
%H A292469 Rémy Sigrist, <a href="/A292469/a292469.png">Representation of the first hundred points of P, with consecutive points joined by a segment</a>
%H A292469 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 A292469 Rémy Sigrist, <a href="/A292469/a292469.txt">C++ program for A292469</a>
%H A292469 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cross_product">Cross product</a>
%H A292469 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dot_product">Dot product</a>
%e A292469 See representation of the first hundred points of P in Links section.
%o A292469 (C++) See Links section.
%Y A292469 Cf. A292470.
%K A292469 sign,look
%O A292469 1,8
%A A292469 _Rémy Sigrist_, Sep 17 2017