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 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). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS See A293681 for the corresponding Y-coordinates. The following diagram depicts the angle t cited in the name: .      P(n)*    . .          | t . .          |  . .          | . .          |. .    P(n-1)* .         / .        / . P(n-2)* This sequence has building features in common with A293539. The study of the first thousand dots shows an alternation of apparently chaotic phases and regular phases where a pattern repeats itself; unlike Langton's ant, this repetitive behavior doesn't last long. It is unknown if eventually a periodic pattern repeating itself infinitely emerges. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program for A293680 Wikipedia, Langton's ant EXAMPLE See representation of first points in Links section. PROG (PARI) See Links section. CROSSREFS Cf. A293539, A293681. Sequence in context: A015504 A055892 A293772 * A293539 A292469 A307011 Adjacent sequences:  A293677 A293678 A293679 * A293681 A293682 A293683 KEYWORD sign,look AUTHOR Rémy Sigrist, Oct 14 2017 STATUS approved

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Last modified October 15 07:56 EDT 2019. Contains 328026 sequences. (Running on oeis4.)