A106796 Fixed point of the morphism 1 -> 1,1,2; 2 -> 3; 3 -> 1,4; 4 -> 1, starting with a(0) = 1.

1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 1, 2, 3

Offset

0,3

Comments

4-symbol substitution for the Pisot characteristic polynomial: x^4 - 2*x^2 - 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 709 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 2
  2 --> 3
  3 --> 1 4
  4 --> 1
-------------
0:   (#=1)
  1
1:   (#=3)
  112
2:   (#=7)
  1121123
3:   (#=16)
  1121123112112314
4:   (#=36)
  112112311211231411211231121123141121
5:   (#=82)
  1121123112112314112112311211231411211121123112112314112112311211231411211121123112

Mathematica

s[1]= {1, 1, 2}; s[2]= {3}; s[3]= {1, 4}; s[4]= {1}; t[b_]:= Flatten[s /@ b];
a[0]= {1}; a[1]= t[p[0]]; a[n_]:= t[a[n-1]];
a[10]

Crossrefs

Cf. A106749, A106795, A106797, A106798.

Sequence in context: A133233 A174430 A116361 * A265743 A082850 A290695

Adjacent sequences: A106793 A106794 A106795 * A106797 A106798 A106799

Keyword

nonn

Author

Roger L. Bagula, May 17 2005

Extensions

Edited by G. C. Greubel, Apr 03 2022

Status

approved