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%I #27 May 15 2021 05:45:20
%S 0,0,1,1,0,0,-1,-1,0,0,1,1,0,0,1,1,0,0,1,1,2,2,1,1,2,2,3,3,2,2,1,1,2,
%T 2,3,3,4,4,3,3,2,2,3,3,2,2,3,3,2,2,1,1,0,0,-1,-1,0,0,-1,-1,0,0,-1,-1,
%U -2,-2,-1,-1,-2,-2,-3,-3,-2,-2,-1,-1,-2,-2,-3
%N Let the starting square of Langton's ant have coordinates (0, 0), with the ant looking in negative x-direction. a(n) is the x-coordinate of the ant after n moves.
%H Rémy Sigrist, <a href="/A274369/b274369.txt">Table of n, a(n) for n = 0..15000</a>
%H Felix Fröhlich, <a href="/A274369/a274369.pdf">Coordinates of Langton's ant</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>.
%F a(n+104) = a(n) + 2 for n > 9975. - _Andrey Zabolotskiy_, Jul 05 2016
%o (Python)
%o # A274369: Langton's ant by _Andrey Zabolotskiy_, Jul 05 2016
%o def ant(n):
%o steps = [(1, 0), (0, 1), (-1, 0), (0, -1)]
%o black = set()
%o x = y = 0
%o position = [(x, y)]
%o direction = 2
%o for _ in range(n):
%o if (x, y) in black:
%o black.remove((x, y))
%o direction += 1
%o else:
%o black.add((x, y))
%o direction -= 1
%o (dx, dy) = steps[direction%4]
%o x += dx
%o y += dy
%o position.append((x, y))
%o return position
%o print([p[0] for p in ant(100)])
%o # change p[0] to p[1] to get y-coordinates
%Y Cf. A274370 (y-coordinate).
%Y Cf. A102358, A102369, A204810, A255938, A261990, A269757.
%K sign,look
%O 0,21
%A _Felix Fröhlich_, Jun 19 2016
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