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 A270643 #9 Jun 21 2025 15:08:06
%S A270643 1,2,2,1,2,1,1,2,2,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,1,2,1,2,2,1,1,2,1,
%T A270643 1,2,2,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,2,1,2,2,1,2,1,1,2,
%U A270643 1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1
%N A270643 The sequence a of 1's and 2's starting with (1,2,2,1) such that a(n) is the length of the (n+3)rd run of a.
%C A270643 See A270641 for a guide to related sequences.
%H A270643 Clark Kimberling, <a href="/A270643/b270643.txt">Table of n, a(n) for n = 1..10000</a>
%F A270643 Conjecture: a(n) = A270642(n+1). - _R. J. Mathar_, Jun 21 2025
%e A270643 a(1) = 1, so the 4th run has length 1, so a(5) must be 1 and a(6) must be 2.
%e A270643 a(2) = 2, so the 5th run has length 2, so a(7) = 1 and a(8) = 2.
%e A270643 a(3) = 2, so the 6th run has length 2, so a(9) = 2 and a(10) = 1.
%e A270643 Globally, the runlength sequence is 1,2,1,1,2,2,1,2,1,1,2,2,1,2,2,1,...., and deleting the first 3 terms leaves the same sequence.
%t A270643 a = {1, 2, 2, 1}; Do[a = Join[a, ConstantArray[If[Last[a] == 1, 2, 1], {a[[n]]}]], {n, 200}]; a (* _Peter J. C. Moses_, Apr 01 2016 *)
%Y A270643 Cf. A000002, A006928, A022300, A270641.
%K A270643 nonn,easy
%O A270643 1,2
%A A270643 _Clark Kimberling_, Apr 06 2016