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A166316 Lexicographically largest binary de Bruijn sequences, B(2,n). 3
2, 12, 232, 63056, 4221224224, 18295693635288736320, 338921575014037816709507133224870496384, 115563265193225535967792084153637585725267224878335215248443107599191173632256 (list; graph; refs; listen; history; text; internal format)



Comment: 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 earliest de Bruijn sequence (Ruskey). de Bruijn sequences can be generated by feedback shift registers (Golomb 1967; Ronse 1984; Skiena 1990, p. 196)."

Python code available with sequence A166315. [From Darse Billings, Oct 18 2009]

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


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

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]

Eric Weisstein's World of Mathematics, de Bruijn Sequence

Wikipedia, de Bruijn Sequence


Example: For n = 3, the last de Bruijn sequence, a(n) = B(2,3), is '11101000' = 232.


Cf. A166315 = 1, 3, 23, 2479, 73743071, ..., Lexicographically earliest de Bruijn sequences (binary complements).

Sequence in context: A011807 A182507 A309615 * A011840 A296462 A125804

Adjacent sequences:  A166313 A166314 A166315 * A166317 A166318 A166319




Darse Billings, Oct 11 2009


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



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Last modified October 15 09:22 EDT 2019. Contains 328026 sequences. (Running on oeis4.)