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

0,7

Comments

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

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

Example

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

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]

Crossrefs

Cf. A106749, A106796, A106797, A106798.

Sequence in context: A307299 A307298 A216674 * A162203 A071455 A288724

Adjacent sequences: A106792 A106793 A106794 * A106796 A106797 A106798

Keyword

nonn

Author

Roger L. Bagula, May 17 2005

Extensions

Edited by G. C. Greubel, Apr 03 2022

Status

approved