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A106797 Fixed point of the morphism 1 -> 1,1,1,1,2,2,3; 2 -> 4,1; 3 -> 2,1,1,1; 4 -> 1,2,1 starting with a(0) = 1.

%I A106797 #19 Apr 05 2022 03:25:14
%S A106797 1,1,1,1,2,2,3,1,1,1,1,2,2,3,1,1,1,1,2,2,3,1,1,1,1,2,2,3,4,1,4,1,2,1,
%T A106797 1,1,1,1,1,1,2,2,3,1,1,1,1,2,2,3,1,1,1,1,2,2,3,1,1,1,1,2,2,3,4,1,4,1,
%U A106797 2,1,1,1,1,1,1,1,2,2,3,1,1,1,1,2,2,3,1,1,1,1,2,2,3,1,1,1,1,2,2,3,4,1,4,1,2
%N A106797 Fixed point of the morphism 1 -> 1,1,1,1,2,2,3; 2 -> 4,1; 3 -> 2,1,1,1; 4 -> 1,2,1 starting with a(0) = 1.
%C A106797 4-symbol substitution of the Pisot characteristic polynomial: x^4 - 4*x^3 - 6*x^2 - x - 1.
%H A106797 G. C. Greubel, <a href="/A106797/b106797.txt">Table of n, a(n) for n = 0..10000</a>
%H A106797 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 4). Also at <a href="https://www.researchgate.net/publication/228561314_Pure_Discrete_Spectrum_for_One-dimensional_Substitution_Systems_of_Pisot_Type">ResearchGate</a>
%H A106797 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e A106797 The first few steps of the substitution are:
%e A106797 Start: 1
%e A106797 Maps:
%e A106797   1 --> 1 1 1 1 2 2 3
%e A106797   2 --> 4 1
%e A106797   3 --> 2 1 1 1
%e A106797   4 --> 1 2 1
%e A106797 -------------
%e A106797 0:   (#=1)
%e A106797   1
%e A106797 1:   (#=7)
%e A106797   1111223
%e A106797 2:   (#=36)
%e A106797   111122311112231111223111122341412111
%t A106797 s[1]= {1,1,1,1,2,2,3}; s[2]= {4,1}; s[3]= {2,1,1,1}; s[4]= {1,2,1};
%t A106797 t[a_]:= Flatten[s /@ a]; p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]]; p[3]
%Y A106797 Cf. A106749, A106795, A106796, A106798.
%K A106797 nonn
%O A106797 0,5
%A A106797 _Roger L. Bagula_, May 17 2005
%E A106797 Edited by _G. C. Greubel_, Apr 03 2022