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.

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, 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, 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

Offset: 0

Author

Roger L. Bagula, May 17 2005

Keywords

• nonn

Comments

4-symbol substitution of the Pisot characteristic polynomial: x^4 - 4*x^3 - 6*x^2 - x - 1.

Examples

			The first few steps of the substitution are:
Start: 1
Maps:
  1 --> 1 1 1 1 2 2 3
  2 --> 4 1
  3 --> 2 1 1 1
  4 --> 1 2 1
-------------
0:   (#=1)
  1
1:   (#=7)
  1111223
2:   (#=36)
  111122311112231111223111122341412111
		

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 709 example 4). Also at ResearchGate
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A106749, A106795, A106796, A106798.

Programs

Mathematica

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[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