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 A229830 #31 Oct 16 2024 21:20:45
%S A229830 1,2,1,2,3,2,1,2,1,2,3,2,1,2,3,4,3,2,1,2,3,2,1,2,1,2,3,2,1,2,1,2,3,2,
%T A229830 1,2,3,4,3,2,1,2,3,2,1,2,1,2,3,2,1,2,3,4,3,2,1,2,3,4,5,4,3,2,1,2,3,4,
%U A229830 3,2,1,2,3,2,1,2,1,2,3,2,1,2,3,4,3,2,1
%N A229830 Trajectory of 1 under the morphism 1 -> 12, 2 -> 1232, 3 -> 123432, 4 -> 12345432, etc.
%C A229830 It appears that records occur at A000111. [This is false. - _Rémy Sigrist_, Nov 15 2018]
%C A229830 The n-th local maximum equals a(n) + 1. - _Rémy Sigrist_, Nov 13 2018
%C A229830 Records at {1, 2, 5, 16, 61, 258, 1161, 5440, 26233, 129282, 648141, 3294864, ...}, which seems to match A104858. - _Michael De Vlieger_, Nov 13 2018
%H A229830 Rémy Sigrist, <a href="/A229830/b229830.txt">Table of n, a(n) for n = 1..8558</a> (7 iterations)
%H A229830 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%t A229830 With[{n = 5}, Take[#, LengthWhile[#, # <= n &] + 1] &@ Nest[Flatten[# /. Array[Last@ # - 1 -> Most[#~Join~Reverse@ Most@ #] &@ Range@ # &, Max@ #, 2]] &, {1}, n]] (* _Michael De Vlieger_, Nov 13 2018 *)
%o A229830 (PARI) my(a = vector(87), n=0); a[1]=1; for (p=1, oo, my(h=1+a[p]); for (v=1, h, a[n++]=v; print1 (v ", "); if (n==#a, break (2))); forstep (v=h-1, 2, -1, a[n++]=v; print1 (v ", "); if (n==#a, break (2)))) \\ _Rémy Sigrist_, Nov 13 2018
%Y A229830 Cf. A007001, A000111.
%K A229830 nonn
%O A229830 1,2
%A A229830 _Franklin T. Adams-Watters_, Dec 08 2013
%E A229830 Data corrected by _Rémy Sigrist_, Nov 13 2018