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A099054
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Arshon's sequence: start from 1 and replace the letters in odd positions using 1 -> 123, 2 -> 231, 3 -> 312 and the letters in even positions using 1 -> 321, 2-> 132, 3 -> 213.
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3
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1, 2, 3, 1, 3, 2, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 2, 3, 1, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 2, 3, 1, 3, 2, 1, 2, 3, 1, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 2, 3, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The first three iterations give 1; 123; 123132312; ... the limiting sequence is shown here. Properties: the sequence is squarefree and cannot be defined by iteration of a morphism.
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REFERENCES
| Sergey Kitaev: There are no Iterated Morphisms that Define the Arshon Sequence and the sigma-Sequence. Journal of Automata, Languages and Combinatorics 8 (2003) 1, 43-0-50.
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LINKS
| James D. Currie: No iterated morphism generates any Arshon Sequence of Odd Order, Discrete Math. 259 (2002), no. 1-3, 277-283.
Sergey Kitaev: There are no Iterated Morphisms that Define the Arshon Sequence and the sigma-Sequence., preprint
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MATHEMATICA
| f[n_List] := Block[{a = {}, l = Length[n], k = 1}, While[k < l + 1, If[ EvenQ[ k], Switch[ n[[k]], 1, AppendTo[a, 321], 2, AppendTo[a, 132], 3, AppendTo[a, 213]], Switch[ n[[k]], 1, AppendTo[a, 123], 2, AppendTo[a, 231], 3, AppendTo[a, 312]]]; k++ ]; Flatten[IntegerDigits /@ a]]; Take[ Nest[f, {1}, 5], 105] (from Robert G. Wilson v Nov 15 2004)
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CROSSREFS
| Cf. A003270. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
Sequence in context: A072457 A063047 A003270 * A071282 A107796 A194308
Adjacent sequences: A099051 A099052 A099053 * A099055 A099056 A099057
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 14 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and John W. Layman (layman(AT)math.vt.edu), Nov 15 2004
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