A106824 Trajectory of 1 under the morphism 1->13, 2->13223, 3->1323.

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

Offset: 0

Author

N. J. A. Sloane, May 20 2005

Keywords

• nonn
• easy

Comments

Only from the 13th term on, this differs from the limit sequence of { 1 -> 131, 2 -> 212, 3 -> 323 } = absolute values of A229215. - M. F. Hasler, Aug 06 2015

Links

• J. M. Dumont and A. Thomas, Digital sum problems and substitutions on a finite alphabet, J. Number Theory, 39 (1991), 351-366.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A229215.

Programs

Maple

S:={1=[1,3],2=[1,3,2,2,3],3=[1,3,2,3]}:subs(S,1):subs(S,%):subs(S,%):subs(S,%):subs(S,%); # all brackets have to be removed. - Emeric Deutsch, simplified by M. F. Hasler, Aug 06 2015
S:={1=(1,3),2=(1,3,2,2,3),3=(1,3,2,3)}: (curry(subs,S)@@6)([1]); # Robert Israel, Aug 06 2015

Mathematica

Nest[ Flatten[ # /. {1 -> {1, 3}, 2 -> {1, 3, 2, 2, 3}, 3 -> {1, 3, 2, 3}}] &, {1}, 5] (* Robert G. Wilson v, Jun 20 2005 *)

PARI

A106824(n,a=[1],S=[[1,3],[1,3,2,2,3],[1,3,2,3]])={while(#aS[i],a)));a} \\ M. F. Hasler, Aug 06 2015

Extensions

More terms from Emeric Deutsch, May 30 2005