A106798 Fixed point of the morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with a(0) = 1.

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

Offset: 0

Author

Roger L. Bagula, May 17 2005

Keywords

• nonn
• less

Comments

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

Examples

			The first few steps of the substitution are:
Start: 1
Maps:
  1 --> 3
  2 --> 1 2 2
  3 --> 1 2
-------------
a(n) = p(2*n)
-------------
0:   (#=1) (p(0))
  1
1:   (#=2) (p(2))
  12
2:   (#=9) (p(4))
  123122122
3:   (#=45) (p(6))
  123122122312212312212231221221231221223122122
		

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. Also at ResearchGate
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A106749, A106795, A106796, A106797.

Programs

Mathematica

s[1]= {3}; s[2]= {1,2,2}; s[3]= {1,2}; t[b_]:= Flatten[s /@ b];
p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]];
a[n_]:= p[2*n];
a[4]

Formula

a(n) = p(2*n), where p(n) maps the fixed point morphism 1 -> 3; 2 -> 1,2,2; 3 -> 1,2, starting with p(0) = 1.

Extensions

Edited by G. C. Greubel, Apr 03 2022