A106797 -id:A106797 - cp's OEIS frontend

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

Roger L. Bagula, May 17 2005

nonn

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

			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

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

Cf. A106749, A106796, A106797, A106798.

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]

Edited by G. C. Greubel, Apr 03 2022

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

Original entry on oeis.org

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

Roger L. Bagula, May 17 2005

nonn

4-symbol substitution for the Pisot characteristic polynomial: x^4 - 2*x^2 - x - 1.

			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

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

Cf. A106749, A106795, A106797, A106798.

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]

Edited by G. C. Greubel, Apr 03 2022

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

Original entry on oeis.org

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

Roger L. Bagula, May 17 2005

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

			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

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

Cf. A106749, A106795, A106796, A106797.

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]

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.

Edited by G. C. Greubel, Apr 03 2022

cp's OEIS Frontend

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.

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

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

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Examples

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Crossrefs

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Mathematica

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Extensions