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A106796 Fixed point of the morphism 1 -> 1,1,2; 2 -> 3; 3 -> 1,4; 4 -> 1, starting with a(0) = 1.

%I A106796 #24 Apr 05 2022 03:26:32
%S A106796 1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,
%T A106796 2,1,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,
%U A106796 1,1,2,1,1,1,2,1,1,2,3,1,1,2,1,1,2,1,1,2,3,1,1,2,1,1,2,3,1,4,1,1,2,1,1,2,3
%N A106796 Fixed point of the morphism  1 -> 1,1,2; 2 -> 3;  3 -> 1,4; 4 -> 1, starting with a(0) = 1.
%C A106796 4-symbol substitution for the Pisot characteristic polynomial: x^4 - 2*x^2 - x - 1.
%H A106796 G. C. Greubel, <a href="/A106796/b106796.txt">Table of n, a(n) for n = 0..10000</a>
%H A106796 Victor F. Sirvent and Boris Solomyak, <a href="https://doi.org/10.4153/CMB-2002-062-3">Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type</a>. Canadian Mathematical Bulletin, 45(4), 2002, 697-710; (page 709 example 3). Also at <a href="https://www.researchgate.net/publication/228561314_Pure_Discrete_Spectrum_for_One-dimensional_Substitution_Systems_of_Pisot_Type">ResearchGate</a>
%H A106796 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e A106796 The first few steps of the substitution are:
%e A106796 Start: 1
%e A106796 Maps:
%e A106796   1 --> 1 1 2
%e A106796   2 --> 3
%e A106796   3 --> 1 4
%e A106796   4 --> 1
%e A106796 -------------
%e A106796 0:   (#=1)
%e A106796   1
%e A106796 1:   (#=3)
%e A106796   112
%e A106796 2:   (#=7)
%e A106796   1121123
%e A106796 3:   (#=16)
%e A106796   1121123112112314
%e A106796 4:   (#=36)
%e A106796   112112311211231411211231121123141121
%e A106796 5:   (#=82)
%e A106796   1121123112112314112112311211231411211121123112112314112112311211231411211121123112
%t A106796 s[1]= {1, 1, 2}; s[2]= {3}; s[3]= {1, 4}; s[4]= {1}; t[b_]:= Flatten[s /@ b];
%t A106796 a[0]= {1}; a[1]= t[p[0]]; a[n_]:= t[a[n-1]];
%t A106796 a[10]
%Y A106796 Cf. A106749, A106795, A106797, A106798.
%K A106796 nonn
%O A106796 0,3
%A A106796 _Roger L. Bagula_, May 17 2005
%E A106796 Edited by _G. C. Greubel_, Apr 03 2022