A227339 Fixed point of the morphism 1 -> 131, 2 -> 312, 3 -> 2.

1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1

Offset

1,2

Comments

Counterexample by Labbé to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes.

In the paper cited, the fixed point is given as acabacacabacab..., this sequence uses 1 for a, 2 for b, and 3 for c.

Links

Table of n, a(n) for n=1..121.

A. Hof, O. Knill, and B. Simon, Singular continuous spectrum for palindromic Schrödinger operators, Comm. Math. Phys., 174 (1995) number 1, pp 149-159.

Sébastien Labbé, A counterexample to a question of Hof, Knill and Simon, arXiv:1307.1589v1 [math.CO], Jul 05 2013

Example

Start: 1
Rules:
  1 --> 131
  2 --> 312
  3 --> 2
-------------
0:   (#=1)
  1
1:   (#=3)
  131
2:   (#=7)
  1312131
3:   (#=17)
  13121313121312131
4:   (#=41)
  13121313121312131213131213121313121312131
5:   (#=99)
  1312131312131213121313121312...
6:   (#=239)
  1312131312131213121313121312...
7:   (#=577)
  1312131312131213121313121312...
- Joerg Arndt, Jul 08 2013

Mathematica

Nest[Flatten[# /. {1 -> {1, 3, 1}, 2 -> {3, 1, 2}, 3 -> {2}}] &, {1}, 5] (* Robert G. Wilson v, Nov 05 2015 *)

Crossrefs

Cf. A010060.

Sequence in context: A361019 A157520 A325116 * A030777 A353375 A056595

Adjacent sequences: A227336 A227337 A227338 * A227340 A227341 A227342

Keyword

nonn,easy

Author

Jonathan Vos Post, Jul 07 2013

Extensions

More terms from Joerg Arndt, Jul 08 2013

Status

approved