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%I #20 Nov 06 2015 10:24:56
%S 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,
%T 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,
%U 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
%N Fixed point of the morphism 1 -> 131, 2 -> 312, 3 -> 2.
%C 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.
%C In the paper cited, the fixed point is given as acabacacabacab..., this sequence uses 1 for a, 2 for b, and 3 for c.
%H A. Hof, O. Knill, and B. Simon, <a href="http://projecteuclid.org/euclid.cmp/1104275098">Singular continuous spectrum for palindromic Schrödinger operators</a>, Comm. Math. Phys., 174 (1995) number 1, pp 149-159.
%H Sébastien Labbé, <a href="http://arxiv.org/abs/1307.1589">A counterexample to a question of Hof, Knill and Simon</a>, arXiv:1307.1589v1 [math.CO], Jul 05 2013
%e Start: 1
%e Rules:
%e 1 --> 131
%e 2 --> 312
%e 3 --> 2
%e -------------
%e 0: (#=1)
%e 1
%e 1: (#=3)
%e 131
%e 2: (#=7)
%e 1312131
%e 3: (#=17)
%e 13121313121312131
%e 4: (#=41)
%e 13121313121312131213131213121313121312131
%e 5: (#=99)
%e 1312131312131213121313121312...
%e 6: (#=239)
%e 1312131312131213121313121312...
%e 7: (#=577)
%e 1312131312131213121313121312...
%e - _Joerg Arndt_, Jul 08 2013
%t Nest[Flatten[# /. {1 -> {1, 3, 1}, 2 -> {3, 1, 2}, 3 -> {2}}] &, {1}, 5] (* _Robert G. Wilson v_, Nov 05 2015 *)
%Y Cf. A010060.
%K nonn,easy
%O 1,2
%A _Jonathan Vos Post_, Jul 07 2013
%E More terms from _Joerg Arndt_, Jul 08 2013
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