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 A293539 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 angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)), say t, satisfies 0 < t <= Pi/2, and in case of a tie, minimize the angle t; a(n) = X-coordinate of P(n). 4
 0, 1, 1, 0, -1, -1, 0, 2, 2, 1, 0, -1, -2, -2, -1, 1, 3, 3, 2, 2, 3, 3, 2, 1, -1, -2, -2, 0, 1, 4, 4, 3, 2, 1, 0, -3, -3, -2, -1, 2, 5, 5, 4, 4, 5, 5, 4, 3, 2, 1, 0, -3, -4, -4, -3, -3, -4, -4, -3, -2, 0, -2, -3, -5, -5, -4, 0, 1, 1, -5, -5, -4, -4, -5, -6, -6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS See A293540 for the Y-coordinate of P(n). The following diagram depicts the angle t cited in the name: .      P(n)*    . .          | t . .          |  . .          | . .          |. .    P(n-1)* .         / .        / . P(n-2)* The sequence P has similarities with Langton's ant: - after an apparently chaotic initial phase, an escape consisting of a repetitive pattern emerges at n = 9118 (see illustrations in Links section), - more formally: P(n+258) = P(n) + (14,-8) for any n >= 9118, - See A274369 and A274370 for the coordinates of Langton's ant, - See also A293207 for other sequences of points with emerging escapes. See also A292469 for a sequence of points with similar construction features. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..12000 Wikipedia, Langton's ant Rémy Sigrist, PARI program for A293539 FORMULA a(n + 258) = a(n) + 14 for any n >= 9118. EXAMPLE See representation of first points in Links section. PROG (PARI) See Links section. CROSSREFS Cf. A274369, A274370, A292469, A293207, A293540. Sequence in context: A055892 A293772 A293680 * A292469 A307011 A285007 Adjacent sequences:  A293536 A293537 A293538 * A293540 A293541 A293542 KEYWORD sign,look AUTHOR Rémy Sigrist, Oct 11 2017 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)