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A275302 Iterations at which Langton's Ant living on triangular tiling passes through the origin. 5
0, 6, 24, 30, 72, 78, 96, 102, 108, 174, 180, 198, 212, 222, 252, 282, 292, 306, 324, 330, 408, 414, 420, 438, 444, 522, 544, 554, 576, 594, 648, 666, 672, 798, 804, 810, 852, 858, 920, 926, 972, 978, 984, 1018, 1024, 1154, 1160, 1178, 1184, 1190, 1208, 1214 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Langton's Ant living on triangular tiling (or, equivalently, hexagonal grid) follows the rules similar to those of the ordinary Langton's ant. On a white cell, turn 60 degrees right, flip the color of the cell, then move forward one unit. On a black cell, turn 60 degrees left, flip the color of the cell, then move forward one unit.

On these iterations pattern becomes symmetric. Orientation of the ant on these iterations is always the same.

Empirically, a(n) ~ c*n^1.207.

LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 1..25000 (calculated using Oleg Nikulin's program)

Wikipedia, Turmite

CROSSREFS

Cf. A102358, A204810, A269757, A275303, A275304, A275305.

Sequence in context: A073120 A147778 A209452 * A201596 A128459 A229292

Adjacent sequences:  A275299 A275300 A275301 * A275303 A275304 A275305

KEYWORD

nonn

AUTHOR

Oleg Nikulin, Jul 22 2016

STATUS

approved

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Last modified October 22 12:22 EDT 2018. Contains 316446 sequences. (Running on oeis4.)