cp's OEIS Frontend

A166316 Lexicographically largest binary de Bruijn sequences, B(2,n).

%I A166316 #23 Feb 16 2025 08:33:11
%S A166316 2,12,232,63056,4221224224,18295693635288736320,
%T A166316 338921575014037816709507133224870496384,
%U A166316 115563265193225535967792084153637585725267224878335215248443107599191173632256
%N A166316 Lexicographically largest binary de Bruijn sequences, B(2,n).
%C A166316 Term a(n) is a cyclical bit string of length 2^n, with every possible substring of length n occurring exactly once.
%C A166316 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)."
%C A166316 Terms grow like Theta(2^(2^n)). - _Darse Billings_, Oct 18 2009
%H A166316 Darse Billings, <a href="/A166316/b166316.txt">Table of n, a(n) for n=1..9</a>
%H A166316 Darse Billings, <a href="/A166315/a166315.py.txt">Python program</a>
%H A166316 F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A166316 F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H A166316 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/deBruijnSequence.html">de Bruijn Sequence</a>
%H A166316 Wikipedia, <a href="http://en.wikipedia.org/wiki/De_Bruijn_sequence">de Bruijn Sequence</a>
%e A166316 For n = 3, the last de Bruijn sequence, a(n) = B(2,3), is '11101000' = 232.
%Y A166316 Cf. A166315 (lexicographically earliest de Bruijn sequences (binary complements)).
%K A166316 base,nonn
%O A166316 1,1
%A A166316 _Darse Billings_, Oct 11 2009
%E A166316 a(6)-a(8) from _Darse Billings_, Oct 18 2009