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

1,2

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.

Sequence in context: A225756 A260143 A353871 * A281500 A041009 A042367

Adjacent sequences: A275300 A275301 A275302 * A275304 A275305 A275306

Keyword

nonn

Author

Oleg Nikulin, Jul 22 2016

Status

approved