A219762 Start with 0; repeatedly apply the map {0->012, 1->120, 2->201} to the odd-numbered terms and {0->210, 1->021, 2->102} to the even-numbered terms.

0, 1, 2, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0

Offset

1,3

Comments

An infinite squarefree sequence over {0,1,2} that is not generated by a CDOL system.

References

A. Salomaa, Jewels of Formal Language Theory. Computer Science Press, Rockville, MD, 1981, p. 16, Problem 13.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) = A099054(n-1) - 1. - Reinhard Zumkeller, Aug 08 2014

Example

0 -> 012 -> 012021201 -> ...

Mathematica

f[lst_] := Replace[MapIndexed[{#1, #2[[1]]}&, lst], {{0, n_} :> If[OddQ[n], {0, 1, 2}, {2, 1, 0}], {1, n_} :> If[OddQ[n], {1, 2, 0}, {0, 2, 1}], {2, n_} :> If[OddQ[n], {2, 0, 1}, {1, 0, 2}]}, 1] // Flatten; Nest[f, {0}, 5] (* Jean-François Alcover, Mar 07 2014 *)

Prog

(Haskell)
a219762 = subtract 1 . a099054 . subtract 1
-- Reinhard Zumkeller, Aug 08 2014

Crossrefs

Sequence in context: A353237 A280830 A068907 * A227696 A033687 A263452

Adjacent sequences: A219759 A219760 A219761 * A219763 A219764 A219765

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2012

Status

approved