A106802 Trajectory of 2 under the morphism 1->{2, 1, 2, 1, 1, 2, 2, 1}, 2->{1, 1, 1, 2, 2, 1, 2}.

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

Offset: 0

Author

Roger L. Bagula, May 17 2005

Keywords

• nonn

References

• T. S. Blyth and E. F. Robertson, Essential Student Algebra: volume 5: Groups: Chapman and Hall, 1986, page 9.

Links

• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A001030, A006338.

Programs

Mathematica

s[1, 1] = {1}; s[2, 1] = {2};; s[1, 2] = {2}; s[2, 2] = {1};; s[1, 3] = {1, 2}; s[2, 3] = {1};; s[1, 4] = {1}; s[2, 4] = {1, 2};; s[1, 5] = {1, 2}; s[2, 5] = {2};; s[1, 6] = {2}; s[2, 6] = {1};; w[i_] = s[1, 1 + Mod[i, 6]] v[i_] = s[2, 1 + Mod[i, 6]] S[1] = Flatten[Table[w[i], {i, 1, 6}]] S[2] = Flatten[Table[v[i], {i, 1, 6}]] t[a_] := Flatten[S /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[3]
Nest[Flatten[#]/.{1->{2,1,2,1,1,2,2,1},2->{1,1,1,2,2,1,2}}&,2,4]//Flatten (* Harvey P. Dale, Apr 09 2019 *)

Extensions

Edited by N. J. A. Sloane, Nov 12 2006