cp's OEIS Frontend

A106795 Fixed point of the morphism 1 -> 1,1,1,1,1,1,2,2,2,3; 2 -> 2,2,3,1,1,1,1; 3 -> 3,1,1,1,2,2, starting with a(0) = 1.

%I A106795 #19 Apr 05 2022 03:24:48
%S A106795 1,1,1,1,1,1,2,2,2,3,1,1,1,1,1,1,2,2,2,3,1,1,1,1,1,1,2,2,2,3,1,1,1,1,
%T A106795 1,1,2,2,2,3,1,1,1,1,1,1,2,2,2,3,1,1,1,1,1,1,2,2,2,3,2,2,3,1,1,1,1,2,
%U A106795 2,3,1,1,1,1,2,2,3,1,1,1,1,3,1,1,1,2,2
%N A106795 Fixed point of the morphism 1 -> 1,1,1,1,1,1,2,2,2,3; 2 -> 2,2,3,1,1,1,1; 3 -> 3,1,1,1,2,2, starting with a(0) = 1.
%C A106795 3-symbol substitution for the characteristic polynomial: x^3 + 9*x^2 - 3*x - 1.
%H A106795 G. C. Greubel, <a href="/A106795/b106795.txt">Table of n, a(n) for n = 0..10000</a>
%H A106795 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 708 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 A106795 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e A106795 The first few steps of the substitution are:
%e A106795 Start: 1
%e A106795 Maps:
%e A106795   1 --> 1 1 1 1 1 1 2 2 2 3
%e A106795   2 --> 2 2 3 1 1 1 1
%e A106795   3 --> 3 1 1 1 2 2
%e A106795 -------------
%e A106795 0:   (#=1)
%e A106795   1
%e A106795 1:   (#=10)
%e A106795   1111112223
%t A106795 s[1]= {1,1,1,1,1,1,2,2,2,3}; s[2]= {2,2,3,1,1,1,1}; s[3]= {3,1,1,1,2,2};
%t A106795 t[a_]:= Flatten[s /@ a]; p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]]; p[3]
%Y A106795 Cf. A106749, A106796, A106797, A106798.
%K A106795 nonn
%O A106795 0,7
%A A106795 _Roger L. Bagula_, May 17 2005
%E A106795 Edited by _G. C. Greubel_, Apr 03 2022