A106750 Define the "Fibonacci" morphism f: 1->12, 2->1 and let a(0) = 2; then a(n+1) = f(a(n)).

2, 1, 12, 121, 12112, 12112121, 1211212112112, 121121211211212112121, 1211212112112121121211211212112112, 1211212112112121121211211212112112121121211211212112121

Offset: 0

Author

N. J. A. Sloane, May 16 2005. Initial term 2 added by N. J. A. Sloane, Jul 05 2012

Keywords

• nonn

Comments

a(n) converges to the Fibonacci word A003842.

a(n) has length Fibonacci(n+1) (cf. A000045).

References

• Berstel, Jean. "Fibonacci words—a survey." In The book of L, pp. 13-27. Springer Berlin Heidelberg, 1986.
• E. Bombieri and J. Taylor, Which distribution of matter diffracts? An initial investigation, in International Workshop on Aperiodic Crystals (Les Houches, 1986), J. de Physique, Colloq. C3, 47 (1986), C3-19 to C3-28.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A106748, A106749, A003842, A000045, A213975, A213976.

Programs

Mathematica

FromDigits /@ NestList[ Flatten[ # /. {1 -> {1, 2}, 2 -> 1}] &, {2}, 8] (* Robert G. Wilson v, May 17 2005 *)

Extensions

More terms from Robert G. Wilson v, May 17 2005