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%I #3 Mar 30 2012 17:31:07
%S 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,
%T 1,3,2,3,1,2,1,3,1,2,3,2,1,3,2,3,1,3,2,1,2,3,1,2,1,3,1,2,3,1,3,2,1,2,
%U 3,2,1,3,1,2,3,1,3,2,3,1,2,3,2,1,3,1,2,1,3,2,1,2,3,1,3,2,3,1,2,1,3,2,1,2,3
%N Arshon's sequence with a different start: start from 3 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.
%t 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, {3}, 5], 105]
%Y Inspired by A099054. Cf. A100336.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Nov 17 2004
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