This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A106824 #24 Dec 04 2018 11:02:48 %S A106824 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 A106824 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 A106824 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 A106824 Trajectory of 1 under the morphism 1->13, 2->13223, 3->1323. %C A106824 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 A106824 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 A106824 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a> %p A106824 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 A106824 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 A106824 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 A106824 (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 A106824 Cf. A229215. %K A106824 nonn,easy %O A106824 0,2 %A A106824 _N. J. A. Sloane_, May 20 2005 %E A106824 More terms from _Emeric Deutsch_, May 30 2005