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Direction where Langton's ant is looking after n moves: 1 if looking in starting direction, 2 if looking 90 degrees clockwise from starting direction, 3 if looking 90 degrees counterclockwise from starting direction, or 4 if looking in direction opposite to starting direction.
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%I #21 May 29 2021 02:12:13

%S 1,2,4,3,1,3,1,2,4,3,4,3,1,2,4,2,1,3,4,3,4,3,1,2,4,2,4,3,1,2,1,3,4,2,

%T 4,2,4,3,1,2,1,2,4,3,1,3,4,2,1,2,1,3,1,2,1,2,4,3,1,3,4,2,1,2,1,2,4,3,

%U 1,3,1,2,4,3,4,2,1,3,1,3,1,2,4,3,4,3,1

%N Direction where Langton's ant is looking after n moves: 1 if looking in starting direction, 2 if looking 90 degrees clockwise from starting direction, 3 if looking 90 degrees counterclockwise from starting direction, or 4 if looking in direction opposite to starting direction.

%F From _Andrey Zabolotskiy_, Oct 11 2016: (Start)

%F Let d(n) = (A255938(n) mod 4). Then:

%F a(n)=1 if d(n)=0,

%F a(n)=2 if d(n)=1,

%F a(n)=4 if d(n)=2,

%F a(n)=3 if d(n)=3.

%F (End)

%Y Cf. A102358, A102369, A204810, A255938, A261990, A269757.

%K nonn

%O 0,2

%A _Felix Fröhlich_, Jul 18 2016

%E More terms from _Andrey Zabolotskiy_, Oct 11 2016