The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A185436 The minimum number of colors required to color an n-bead bracelet so that each bead can be uniquely identified by its color and the color(s) of its two immediately-adjacent neighbors. 1
1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
I am not sure whether or not this sequence is just the biggest number k for which A002411(k) is less than or equal to n. Clearly that forms a lower bound, since it is the number of 3-symbol strings where reversing the string doesn't matter.
LINKS
Canadian Mathematics Olympiad, Problem 2, 1984.
MathLearning.org, Solution [gives A185437]
EXAMPLE
For example, the string AABABBBCCC colors a bracelet of 10 beads using 3 symbols. No two beads have the same color and neighbors with the same set of colors. In this problem, the order in which the neighbors' colors occur doesn't matter (because the bracelet can be turned over). So the string ABBABCBCAC wouldn't work, because we can't distinguish between the second and third beads (ABB and BBA). We can't do this with only 2 colors, so a(10) = 3.
CROSSREFS
Sequence in context: A065682 A065681 A121242 * A025794 A354760 A025793
KEYWORD
nonn
AUTHOR
Jack W Grahl, Jan 27 2011
EXTENSIONS
Definition and example changed (per a comment by Wouter Meeussen) to refer to the ring of beads using the term "bracelet," rather than "necklace," since turning the ring over is allowed. - Jon E. Schoenfield, Sep 18 2013
More terms from Bert Dobbelaere, Jul 17 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 23:34 EDT 2024. Contains 373432 sequences. (Running on oeis4.)