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.

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

Offset: 0

Author

Roger L. Bagula, May 17 2005

Keywords

• nonn

Comments

3-symbol substitution for the characteristic polynomial: x^3 + 9*x^2 - 3*x - 1.

Examples

			The first few steps of the substitution are:
Start: 1
Maps:
  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
-------------
0:   (#=1)
  1
1:   (#=10)
  1111112223
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Victor F. Sirvent and Boris Solomyak, Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type. Canadian Mathematical Bulletin, 45(4), 2002, 697-710; (page 708 example 3). Also at ResearchGate
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A106749, A106796, A106797, A106798.

Programs

Mathematica

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[a_]:= Flatten[s /@ a]; p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]]; p[3]

Extensions

Edited by G. C. Greubel, Apr 03 2022