|
Search: id:A099054
|
|
|
| A099054 |
|
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. |
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
The first three iterations give 1; 123; 123132312; ... the limiting sequence is shown here. Properties: the sequence is square-free and cannot be defined by iteration of a morphism.
|
|
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.
|
|
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
|
|
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)
|
|
CROSSREFS
|
Cf. A003270. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
Sequence in context: A072457 A063047 A003270 this_sequence A071282 A107796 A039702
Adjacent sequences: A099051 A099052 A099053 this_sequence A099055 A099056 A099057
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 14 2004
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and John W. Layman (layman(AT)math.vt.edu), Nov 15 2004
|
|
|
Search completed in 0.002 seconds
|
