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.

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

Offset

1,3

Comments

Apparently, every lattice point will be marked.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, Illustration of the first 200000 marks, with color change every 20000 marks

Paul Tek, PERL program for this sequence

Paul Tek, Illustration of the first 100000 marks with cyclic colors (red - green - blue)

Paul Tek, Illustration of the first 100000 marks with cyclic colors: red component

Paul Tek, Illustration of the first 100000 marks with cyclic colors: green component

Paul Tek, Illustration of the first 100000 marks with cyclic colors: blue component

Index entries for sequences related to A2 = hexagonal = triangular lattice

Example

This diagram depicts the first 9 marks:
  \ / \ / \ /
--4---5---.--
  / \ / \ / \
-7---1---2---8-
  \ / \ / \ / \
--6---3---9--
  / \ / \ / \
a(1) = number of steps between 1st and 2nd marks = 1;
a(2) = number of steps between 2nd and 3rd marks = 1;
a(3) = number of steps between 3rd and 4th marks = 2;
a(4) = number of steps between 4th and 5th marks = 1;
a(5) = number of steps between 5th and 6th marks = 2;
a(6) = number of steps between 6th and 7th marks = 1;
a(7) = number of steps between 7th and 8th marks = 3;
a(8) = number of steps between 8th and 9th marks = 1.

Prog

(Perl) See Links section.

Crossrefs

Cf. A001334, A125852.

Sequence in context: A282903 A332677 A090329 * A340830 A027353 A027352

Adjacent sequences: A224873 A224874 A224875 * A224877 A224878 A224879

Keyword

nonn,walk

Author

Paul Tek, Jul 23 2013

Status

approved