A105203 Trajectory of 1 under the morphism f: 1->{1,2,1}, 2->{2,3,2}, 3->{3,1,3}.

1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 1, 3, 1, 2, 1, 3, 1, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 1, 3, 1, 2, 1, 3, 1, 3, 2, 3, 2, 3, 1, 3

Offset: 0

Author

Roger L. Bagula, Apr 09 2005

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19682
• F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104; page 96, section 4.10.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A003462, A062153, A073058, A105141, A105202.

Programs

Mathematica

Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {2, 3, 2}, 3 -> {3, 1, 3}}] &, {1}, 5] (* Robert G. Wilson v, Apr 12 2005 *)

Scheme

(define (A105203 n) (if (zero? n) 1 (A105202 (+ n (A003462 (+ 1 (A062153 n))))))) ;; Antti Karttunen, Aug 12 2017

Formula

a(0) = 1; and for n > 1, a(n) = A105202(n+A003462(1+A062153(n))). - Antti Karttunen, Aug 12 2017

Extensions

More terms from Robert G. Wilson v, Apr 12 2005