A106036 -id:A106036 - cp's OEIS frontend

A106035 The "Octanacci" sequence: Trajectory of 1 under the morphism 1->{1,2,1}, 2->{1}.

1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2

Offset: 0

Roger L. Bagula, May 05 2005

nonn

Silver mean chain substitution sequence: characteristic polynomial = -x^2+2*x+1.
A space-filling lattice is given by: bb = aa /. 1 -> {-0.4142135623730951, 2.414213562373095} /. 2 -> {1,-0.414213562373095`} /. 3 -> 0; ListPlot[FoldList[Plus, {0, 0}, bb], PlotRange -> All, PlotJoined -> False, Axes -> False];
The sequence is S_oo where S_0 = 2, S_1 = 1; S_{n+2} = S_{n+1} S_n S_{n+1}. Used to construct the "labyrinth" tiling. - N. J. A. Sloane, Mar 13 2019

G. C. Greubel, Table of n, a(n) for n = 0..1392
M. Baake and R. V. Moody, Self-Similar Measures for Quasicrystals, in Directions in Mathematical Quasicrystals (eds. M. Baake and R. V. Moody), CRM Monograph Series, vol. 13, AMS, Providence, RI (2000), pp. 1-42; arXiv:math/0008063 [math.MG], 2000.
Clément Sire, Rémy Mosseri, and Jean-François Sadoc, Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling, Journal de Physique 50.24 (1989): 3463-3476. See Eq. 2; HAL Id : jpa-00211156.
Index entries for sequences that are fixed points of mappings

Cf. A085301, A106036.

See A324772 for version over {0,1}.

f(1):= (1, 2, 1): f(2):= (1): A:= [1]:
for i from 1 to 6 do A:= map(f, A) od:
A; # - N. J. A. Sloane, Mar 13 2019

s[1] = {1, 2, 1}; s[2] = {1}; s[3] = {}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[6]
Nest[Function[l, Flatten[l/.{1->{1, 2, 1}, 2->{1}}]], {1}, 6] (* Vincenzo Librandi, Mar 14 2019 *)
SubstitutionSystem[{1->{1,2,1},2->{1}},{1},{6}]//Flatten (* Harvey P. Dale, Nov 20 2021 *)

A138670 Indices of 0's in Stewart's choral sequence.

Original entry on oeis.org

0, 1, 3, 4, 6, 9, 10, 12, 13, 15, 18, 19, 21, 24, 27, 28, 30, 31, 33, 36, 37, 39, 40, 42, 45, 46, 48, 51, 54, 55, 57, 58, 60, 63, 64, 66, 69, 72, 73, 75, 78, 81, 82, 84, 85, 87, 90, 91, 93, 94, 96, 99, 100, 102, 105, 108, 109, 111, 112, 114, 117, 118, 120, 121

Offset: 0

Joel Reyes Noche (joel.noche(AT)up.edu.ph), Mar 26 2008

Conjecture: essentially partial sums of A106036 (verified for n <= 10000). - Sean A. Irvine, Jul 19 2022

Sean A. Irvine, Table of n, a(n) for n = 0..9999

Cf. A106036, A116178, A138671.

The set {k*3^(m+1) + (3^m-1)/2 with k >= 0 and m >= 1}.

More terms from Sean A. Irvine, Jul 19 2022

cp's OEIS Frontend

A106035 The "Octanacci" sequence: Trajectory of 1 under the morphism 1->{1,2,1}, 2->{1}.

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