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A166315 Lexicographically earliest binary de Bruijn sequences, B(2,n). 4
1, 3, 23, 2479, 73743071, 151050438420815295, 1360791906900646753867474206897715071, 228824044090659455778900855050322128002759787305348791014476408721956007679 (list; graph; refs; listen; history; text; internal format)



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)."

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


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

Darse Billings, Python program

Mathworld, de Bruijn Sequence

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]

Wikipedia, de Bruijn Sequence


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


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

Sequence in context: A009593 A009818 A210734 * A113577 A224700 A264929

Adjacent sequences:  A166312 A166313 A166314 * A166316 A166317 A166318




Darse Billings, Oct 11 2009


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



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Last modified January 17 04:22 EST 2019. Contains 319206 sequences. (Running on oeis4.)