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A224876 On an hexagonal lattice, repeatedly: mark the current point and then move forward to the nearest unmarked point and then rotate 120 degrees clockwise. a(n) gives the number of steps between the n-th and (n+1)-th marks.

%I A224876 #32 Oct 13 2019 18:07:11
%S A224876 1,1,2,1,2,1,3,1,3,1,4,1,4,1,5,1,5,1,6,1,3,1,3,4,3,4,3,5,1,3,1,6,3,6,
%T A224876 3,7,1,6,1,8,1,6,1,7,3,8,3,8,1,8,1,9,1,9,1,10,1,2,1,3,10,3,10,3,1,2,1,
%U A224876 12,1,3,1,5,1,2,1,12,1,3,1,5,9,4,11,1,2,1
%N A224876 On an hexagonal lattice, repeatedly: mark the current point and then move forward to the nearest unmarked point and then rotate 120 degrees clockwise. a(n) gives the number of steps between the n-th and (n+1)-th marks.
%C A224876 Apparently, every lattice point will be marked.
%H A224876 Paul Tek, <a href="/A224876/b224876.txt">Table of n, a(n) for n = 1..10000</a>
%H A224876 Paul Tek, <a href="/A224876/a224876.png">Illustration of the first 200000 marks, with color change every 20000 marks</a>
%H A224876 Paul Tek, <a href="/A224876/a224876.txt">PERL program for this sequence</a>
%H A224876 Paul Tek, <a href="/A224876/a224876_1.png">Illustration of the first 100000 marks with cyclic colors (red - green - blue)</a>
%H A224876 Paul Tek, <a href="/A224876/a224876_2.png">Illustration of the first 100000 marks with cyclic colors: red component</a>
%H A224876 Paul Tek, <a href="/A224876/a224876_3.png">Illustration of the first 100000 marks with cyclic colors: green component</a>
%H A224876 Paul Tek, <a href="/A224876/a224876_4.png">Illustration of the first 100000 marks with cyclic colors: blue component</a>
%H A224876 <a href="/index/Aa#A2">Index entries for sequences related to A2 = hexagonal = triangular lattice</a>
%e A224876 This diagram depicts the first 9 marks:
%e A224876   \ / \ / \ /
%e A224876 --4---5---.--
%e A224876   / \ / \ / \
%e A224876 -7---1---2---8-
%e A224876   \ / \ / \ / \
%e A224876 --6---3---9--
%e A224876   / \ / \ / \
%e A224876 a(1) = number of steps between 1st and 2nd marks = 1;
%e A224876 a(2) = number of steps between 2nd and 3rd marks = 1;
%e A224876 a(3) = number of steps between 3rd and 4th marks = 2;
%e A224876 a(4) = number of steps between 4th and 5th marks = 1;
%e A224876 a(5) = number of steps between 5th and 6th marks = 2;
%e A224876 a(6) = number of steps between 6th and 7th marks = 1;
%e A224876 a(7) = number of steps between 7th and 8th marks = 3;
%e A224876 a(8) = number of steps between 8th and 9th marks = 1.
%o A224876 (Perl) See Links section.
%Y A224876 Cf. A001334, A125852.
%K A224876 nonn,walk
%O A224876 1,3
%A A224876 _Paul Tek_, Jul 23 2013