

A275303


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


4



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
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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: A032806 A225756 A260143 * A281500 A041009 A042367
Adjacent sequences: A275300 A275301 A275302 * A275304 A275305 A275306


KEYWORD

nonn


AUTHOR

Oleg Nikulin, Jul 22 2016


STATUS

approved



