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A166315
Lexicographically earliest binary de Bruijn sequences, B(2,n).
7
1, 3, 23, 2479, 73743071, 151050438420815295, 1360791906900646753867474206897715071, 228824044090659455778900855050322128002759787305348791014476408721956007679
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 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
LINKS
William Boyles, Table of n, a(n) for n = 1..11 (first 9 terms from Darse Billings)
Darse Billings, Python program
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
EXAMPLE
Example: For n = 3, the first de Bruijn sequence, a(n) = B(2,3), is '00010111' = 23.
CROSSREFS
Cf. A166316 (Lexicographically largest de Bruijn sequences (binary complements)).
Sequence in context: A351107 A009818 A210734 * A371346 A347680 A113577
KEYWORD
base,nonn
AUTHOR
Darse Billings, Oct 11 2009
EXTENSIONS
a(6)-a(8) from Darse Billings, Oct 18 2009
STATUS
approved