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 A092400 #25 Apr 11 2025 03:30:47
%S A092400 1,1,2,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,2,1,2,1,2,1,2,1,1,1,1,2,1,2,1,1,
%T A092400 1,1,2,1,2,1,2,1,2,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,2,1,1,
%U A092400 1,1,2,1,2,1,1,1,1,2,1,2,1,2,1,2,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,2,1,2,1,2,1
%N A092400 Fixed point of the morphism 1 -> 1121211, 2 -> 1121212121211, starting from a(1) = 1.
%C A092400 Length of n-th run of identical symbols in A051069.
%H A092400 Amiram Eldar, <a href="/A092400/b092400.txt">Table of n, a(n) for n = 1..10000</a>
%H A092400 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>.
%F A092400 Sum_{k=1..n} a(k) = A007417(n).
%F A092400 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4/3. - _Amiram Eldar_, Apr 11 2025
%t A092400 Nest[ Function[ l, {Flatten[(l /. {1 -> {1, 1, 2, 1, 2, 1, 1}, 2 -> {1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1}})]}], {1}, 3] (* _Robert G. Wilson v_, Feb 26 2005 *)
%o A092400 (Python)
%o A092400 from sympy import integer_log
%o A092400 def A007417(n):
%o A092400 def f(x): return n+x-sum(((m:=x//9**i)-2)//3+(m-1)//3+2 for i in range(integer_log(x,9)[0]+1))
%o A092400 m, k = n, f(n)
%o A092400 while m != k: m, k = k, f(k)
%o A092400 return m
%o A092400 def A092400(n): return A007417(n)-A007417(n-1) if n>1 else 1 # _Chai Wah Wu_, Feb 16 2025
%Y A092400 Cf. A007417, A051069.
%K A092400 easy,nonn
%O A092400 1,3
%A A092400 _Philippe Deléham_, Mar 21 2004
%E A092400 More terms from _Robert G. Wilson v_, Feb 26 2005