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A275303 Iterations at which Langton's Ant living on triangular tiling reaches the distance of n from the origin for the first time. 4

%I #27 Nov 02 2016 05:34:15

%S 1,2,3,14,15,48,53,136,145,362,375,474,491,724,745,1904,1921,2234,

%T 2267,2362,2383,2500,2537,2786,2811,3542,3575,8304,8325,8432,8501,

%U 8948,8989,14858,14911,15256,15309,18258,18367,21804,22021,22380,22453,23222,23279

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

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

%C 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]

%H Andrey Zabolotskiy, <a href="/A275303/b275303.txt">Table of n, a(n) for n = 1..1500</a> (calculated using _Oleg Nikulin_'s program)

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

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

%K nonn

%O 1,2

%A _Oleg Nikulin_, Jul 22 2016

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Last modified April 25 01:06 EDT 2024. Contains 371964 sequences. (Running on oeis4.)