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 A157684 #7 Jun 02 2025 01:25:35
%S A157684 1,1,1,1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,7,8,8,9,9,9,9,10,10,10,11,
%T A157684 11,12,12,12,13,13,13,13,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,
%U A157684 19,19,19,20,20,21,21,21,22,22,22,22,23,23,23,24,24,25,25,25,26,26,26,27
%N A157684 a(n)=#{1<=k<=n : [K(k),K(k+1)]=[1,2]} where K=A000002.
%C A157684 Presumably a(n)=n/3+o(n)
%F A157684 a(n)=sum(k=1,n,(K(k+1)-1)*(K(k+1)-K(k))) where K(k)=A000002(k).
%o A157684 (PARI) a(n)=sum(k=1,n,if(abs(A000002(k)-1)+abs(A000002(k+1)-2),0,1))
%Y A157684 Cf. A157685, A157686, A157687
%K A157684 nonn
%O A157684 1,5
%A A157684 _Benoit Cloitre_, Mar 04 2009