A224876 - OEIS

%I #32 Oct 13 2019 18:07:11

%S 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 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 12,1,3,1,5,1,2,1,12,1,3,1,5,9,4,11,1,2,1

%N 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 Apparently, every lattice point will be marked.

%H Paul Tek, <a href="/A224876/b224876.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Tek, <a href="/A224876/a224876.png">Illustration of the first 200000 marks, with color change every 20000 marks</a>

%H Paul Tek, <a href="/A224876/a224876.txt">PERL program for this sequence</a>

%H Paul Tek, <a href="/A224876/a224876_1.png">Illustration of the first 100000 marks with cyclic colors (red - green - blue)</a>

%H Paul Tek, <a href="/A224876/a224876_2.png">Illustration of the first 100000 marks with cyclic colors: red component</a>

%H Paul Tek, <a href="/A224876/a224876_3.png">Illustration of the first 100000 marks with cyclic colors: green component</a>

%H Paul Tek, <a href="/A224876/a224876_4.png">Illustration of the first 100000 marks with cyclic colors: blue component</a>

%H <a href="/index/Aa#A2">Index entries for sequences related to A2 = hexagonal = triangular lattice</a>

%e This diagram depicts the first 9 marks:

%e   \ / \ / \ /

%e --4---5---.--

%e   / \ / \ / \

%e -7---1---2---8-

%e   \ / \ / \ / \

%e --6---3---9--

%e   / \ / \ / \

%e a(1) = number of steps between 1st and 2nd marks = 1;

%e a(2) = number of steps between 2nd and 3rd marks = 1;

%e a(3) = number of steps between 3rd and 4th marks = 2;

%e a(4) = number of steps between 4th and 5th marks = 1;

%e a(5) = number of steps between 5th and 6th marks = 2;

%e a(6) = number of steps between 6th and 7th marks = 1;

%e a(7) = number of steps between 7th and 8th marks = 3;

%e a(8) = number of steps between 8th and 9th marks = 1.

%o (Perl) See Links section.

%Y Cf. A001334, A125852.

%K nonn,walk

%O 1,3

%A _Paul Tek_, Jul 23 2013