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Search: id:A112658
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| A112658 |
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Dean's Word: Omega 2,1: the trajectory of 0 -> 01, 1 -> 21, 2 -> 03, 3 -> 23. |
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+0
2
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| 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 1, 0
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Even-indexed terms of this sequence are the sequence A099545. - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Jan 02 2006
Fractal sequence: odd terms are 0, 2, 0, 2,...; the subsets formed with the terms of index (2^i)n, with i>0, are identical: a(2n)=a(4n)=a(8n)=a(16n)=... - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Jan 02 2006
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REFERENCES
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Dean, Richard A. 1965. A sequence without repeats on x, ..., Amer. Math. Monthly 72, 383-385. MR 31 #350.
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LINKS
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George F. McNulty, Avoidable Words
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FORMULA
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It should be easy to prove that a(4n) = 0, a(4n+2) = 2, a(8n+1) = 1, a(8n+5) = 3, a(4n+3) = a(2n+1). This would imply that a(2n) = 2(n mod 2), a(2n+1) = 1 + 2*A014707(n), with A014707(n) the classical paperfolding curve. - Ralf Stephan, Dec28 2005
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MATHEMATICA
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Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {2, 1}, 2 -> {0, 3}, 3 -> {2, 3}}] &, {0}, 7] (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 27 2005)
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CROSSREFS
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Sequence in context: A131358 A117901 A074984 this_sequence A025581 A025669 A025676
Adjacent sequences: A112655 A112656 A112657 this_sequence A112659 A112660 A112661
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KEYWORD
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nonn
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AUTHOR
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Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Dec 27 2005
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