A106824 - OEIS

%I #24 Dec 04 2018 11:02:48

%S 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,

%T 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,

%U 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

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

%C 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

%H J. M. Dumont and A. Thomas, <a href="https://doi.org/10.1016/0022-314X(91)90054-F">Digital sum problems and substitutions on a finite alphabet</a>, J. Number Theory, 39 (1991), 351-366.

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%p 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

%p 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

%t 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 *)

%o (PARI) A106824(n,a=[1],S=[[1,3],[1,3,2,2,3],[1,3,2,3]])={while(#a<n,a=concat(apply(i->S[i],a)));a} \\ _M. F. Hasler_, Aug 06 2015

%Y Cf. A229215.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 20 2005

%E More terms from _Emeric Deutsch_, May 30 2005