A275303 Iterations at which Langton's Ant living on triangular tiling reaches the distance of n from the origin for the first time.

1, 2, 3, 14, 15, 48, 53, 136, 145, 362, 375, 474, 491, 724, 745, 1904, 1921, 2234, 2267, 2362, 2383, 2500, 2537, 2786, 2811, 3542, 3575, 8304, 8325, 8432, 8501, 8948, 8989, 14858, 14911, 15256, 15309, 18258, 18367, 21804, 22021, 22380, 22453, 23222, 23279

Offset: 1

Author

Oleg Nikulin, Jul 22 2016

Keywords

• nonn

Comments

The distance is defined as the number of steps needed to reach the origin (analog of Manhattan distance).

a(n) ~ c*n^2; however, the first several hundreds of terms are very well described by the approximate formula c'*n^(2.8). [amended by Andrey Zabolotskiy, Oct 09 2016 and Nov 02 2016]

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 1..1500 (calculated using _Oleg Nikulin_'s program)
• Wikipedia, Turmite

Crossrefs

Cf. A269757, A275302, A275304 (first differences), A275305.