login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A166315 Lexicographically smallest binary de Bruijn sequences, B(2,n). 4
1, 3, 23, 2479, 73743071, 151050438420815295, 1360791906900646753867474206897715071, 228824044090659455778900855050322128002759787305348791014476408721956007679 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Term a(n) is a cyclical bit string of length 2^n, with every possible substring of length n occurring exactly once.

Mathworld (http://mathworld.wolfram.com/deBruijnSequence.html) says: "Every de Bruijn sequence corresponds to an Eulerian cycle on a de Bruijn graph. Surprisingly, it turns out that the lexicographic sequence of Lyndon words of lengths divisible by n gives the lexicographically smallest de Bruijn sequence (Ruskey). de Bruijn sequences can be generated by feedback shift registers (Golomb 1967; Ronse 1984; Skiena 1990, p. 196)."

Terms grow like Theta(2^(2^n)). - Darse Billings, Oct 18 2009

LINKS

Darse Billings, Table of n, a(n) for n=1..9

Darse Billings, Python program

Mathworld, de Bruijn Sequence

F. Ruskey, Information on necklaces, unlabelled necklaces, Lyndon words, de Bruijn sequences

Wikipedia, de Bruijn Sequence

EXAMPLE

Example: For n = 3, the first de Bruijn sequence, a(n) = B(2,3), is '00010111' = 23.

CROSSREFS

Cf. A166316 = 2, 12, 232, 63056, 4221224224, ..., Lexicographically largest de Bruijn sequences (binary complements).

Sequence in context: A009593 A009818 A210734 * A113577 A224700 A204578

Adjacent sequences:  A166312 A166313 A166314 * A166316 A166317 A166318

KEYWORD

base,nonn

AUTHOR

Darse Billings, Oct 11 2009

EXTENSIONS

Added three more terms, a(6)-a(8) Darse Billings, Oct 18 2009

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 24 07:21 EST 2014. Contains 249871 sequences.