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

0,1

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

Mathematica

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

Crossrefs

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

Sequence in context: A181867 A231611 A171510 * A258821 A124916 A007418

Adjacent sequences: A106747 A106748 A106749 * A106751 A106752 A106753

Keyword

nonn

Author

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

Extensions

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

Status

approved