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A166315
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Lexicographically earliest binary de Bruijn sequences, B(2,n).
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7
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OFFSET
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1,2
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COMMENTS
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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)."
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LINKS
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EXAMPLE
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Example: For n = 3, the first de Bruijn sequence, a(n) = B(2,3), is '00010111' = 23.
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CROSSREFS
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Cf. A166316 (Lexicographically largest de Bruijn sequences (binary complements)).
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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