A105969 Fixed point of the morphism 1 -> 123, 2 -> 212, 3 -> 345, 4 -> 434, 5 -> 561, 6 -> 656, starting from a(0) = 1.

1, 2, 3, 2, 1, 2, 3, 4, 5, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 1, 4, 3, 4, 3, 4, 5, 4, 3, 4, 5, 6, 1, 6, 5, 6, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 2, 1, 2, 1, 2, 3

Offset

0,2

Comments

Six-symbol substitution modeled on a hexagon loop.

Characteristic Polynomial: x^6-9*x^5+30*x^4-46*x^3+36*x^2-21*x+9=0 L-system shown as: bb = a /. 1 -> {1, 0} /. 2 -> {0.5, 0.8660254037844386} /. 3 -> {-0.5,0.8660254037844386} /. 4 -> {-1, 0} /. 5 -> {-0.5, -0.8660254037844386} /. 6 -> {0.5, -0.8660254037844386}; ListPlot[FoldList[Plus, {0, 0}, bb], PlotRange -> All, PlotJoined -> True, Axes -> False];

Links

Table of n, a(n) for n=0..104.

Index entries for sequences that are fixed points of mappings

Mathematica

Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 3}, 2 -> {2, 1, 2}, 3 -> {3, 4, 5}, 4 -> {4, 3, 4}, 5 -> {5, 6, 1}, 6 -> {6, 5, 6}} &], {1}, 5]] (* Robert G. Wilson v, May 07 2005 *)

Crossrefs

Sequence in context: A118121 A006968 A058207 * A275892 A163530 A114409

Adjacent sequences: A105966 A105967 A105968 * A105970 A105971 A105972

Keyword

nonn

Author

Roger L. Bagula, Apr 28 2005

Extensions

Edited and corrected by Robert G. Wilson v, May 07 2005

Status

approved