A106796 - OEIS

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

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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: (#=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: A174430 A116361 A375571 * 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