A275302 Iterations at which Langton's Ant living on triangular tiling passes through the origin.

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

Offset: 1

Author

Oleg Nikulin, Jul 22 2016

Keywords

• nonn

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.