Darse Billings has authored 3 sequences.
A166315
Lexicographically earliest binary de Bruijn sequences, B(2,n).
Original entry on oeis.org
1, 3, 23, 2479, 73743071, 151050438420815295, 1360791906900646753867474206897715071, 228824044090659455778900855050322128002759787305348791014476408721956007679
Offset: 1
Example: For n = 3, the first de Bruijn sequence, a(n) = B(2,3), is '00010111' = 23.
- William Boyles, Table of n, a(n) for n = 1..11 (first 9 terms from Darse Billings)
- Darse Billings, Python program
- Frank Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
- Frank Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
- Frank Ruskey, Combinatorial Generation (pdf, 2003).
- SageMath, Python code
- Eric Weisstein's World of Mathematics, de Bruijn Sequence
- Wikipedia, de Bruijn Sequence
Cf.
A166316 (Lexicographically largest de Bruijn sequences (binary complements)).
A166316
Lexicographically largest binary de Bruijn sequences, B(2,n).
Original entry on oeis.org
2, 12, 232, 63056, 4221224224, 18295693635288736320, 338921575014037816709507133224870496384, 115563265193225535967792084153637585725267224878335215248443107599191173632256
Offset: 1
For n = 3, the last de Bruijn sequence, a(n) = B(2,3), is '11101000' = 232.
- Darse Billings, Table of n, a(n) for n=1..9
- Darse Billings, Python program
- 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
Cf.
A166315 (lexicographically earliest de Bruijn sequences (binary complements)).
Original entry on oeis.org
1, 2, 12, 360, 151200, 2095632000, 7551819475200000, 7286477990937425280000000, 16326289449604557795871699200000000000, 48235535472088469901966394717904245153920000000000000, 1927704301314417844667587261525561805756528196513768633600000000000000000
Offset: 1
a(5) = 1^7 * 2^5 * 3^3 * 5^2 * 7^1 = 151200.
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s={};Do[p1=Join[{1},Prime[Range[n-1]]];AppendTo[s,Product[p1[[k]]^p1[[n-k+1]],{k,n}]],{n,11}];s (* James C. McMahon, Feb 27 2025 *)
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