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).
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
Offset: 1
Examples
See representation of the first hundred points of P in Links section.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..1000
- Rémy Sigrist, Representation of the first hundred points of P, with consecutive points joined by a segment
- Rémy Sigrist, Representation of the first 500 points of P, with consecutive points joined by a segment
- Rémy Sigrist, C++ program for A292469
- Wikipedia, Cross product
- Wikipedia, Dot product
Crossrefs
Cf. A292470.
Comments