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A275302 Iterations at which Langton's Ant living on triangular tiling passes through the origin. 5

%I

%S 0,6,24,30,72,78,96,102,108,174,180,198,212,222,252,282,292,306,324,

%T 330,408,414,420,438,444,522,544,554,576,594,648,666,672,798,804,810,

%U 852,858,920,926,972,978,984,1018,1024,1154,1160,1178,1184,1190,1208,1214

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

%C 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.

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

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

%H Andrey Zabolotskiy, <a href="/A275302/b275302.txt">Table of n, a(n) for n = 1..25000</a> (calculated using _Oleg Nikulin_'s program)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Turmite">Turmite</a>

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

%K nonn

%O 1,2

%A _Oleg Nikulin_, Jul 22 2016

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)