A293680 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 i < j < k, P(k) does not lie on the vector (P(i), P(j)), and for any n > 2, P(n) is the closest lattice point 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, minimize the angle t; a(n) = X-coordinate of P(n).
0, 1, 1, 0, -1, -1, 0, 2, 2, 1, 0, -1, -2, -2, -1, 1, 3, 3, 2, 1, -1, -2, -3, -3, -2, -1, 1, 2, 4, 4, 3, 2, 0, -3, -4, -4, -3, -2, -1, 1, 2, 3, 4, 4, 3, 1, -2, -5, -5, -4, -5, -6, -6, -5, -4, -2, -1, 1, 2, 3, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 1, -2, -7, -7, -6, -7
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, Representation of P(n) for n=1..1000, with lines joining consecutive points and patterns repeated at least three times colored in red/green/blue
- Rémy Sigrist, Representation of P(n) for n=1..18698, with patterns repeated at least three times colored in red/green/blue
- Rémy Sigrist, PARI program for A293680
- Wikipedia, Langton's ant
Programs
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PARI
See Links section.
Comments