A293729 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 at integer distance to P(n-1) such that the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)), say t, satisfies 0 < t < Pi, and in case of a tie, maximize the angle t; a(n) = X-coordinate of P(n).
0, 1, 1, 0, 0, 1, 1, 0, 0, 1, -3, -3, -2, -2, -4, -4, -1, -1, -5, -5, -2, -3, -3, -2, -2, -3, -3, -2, -2, -3, 1, 1, 0, 0, 2, 2, -1, -1, 3, 3, -1, -1, 0, 0, -2, -5, -4, -4, -5, -5, -4, -4, -5, -1, -1, -6, -6, -3, -4, -4, -3, -3, -4, -4, -1, -2, -2, -1, -1, -2
Offset: 1
Examples
See representation of first points in Links section.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, Representation of P(n) for n=1..100, with lines joining consecutive points
- Rémy Sigrist, Colorized representation of P(n) for n=1..200000
- Rémy Sigrist, Representation of P(n) with duplicate pattern highlighted
- Rémy Sigrist, Representation of the variant P'(n) for n=1..10000
- Rémy Sigrist, PARI program for A293729
Comments