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 A110011 #12 Sep 04 2024 17:48:40
%S A110011 1,2,3,4,5,6,7,8,8,7,8,8,7,8,7,8,8,7,8,8,9,8,7,8,8,7,8,7,8,8,7,8,8,7,
%T A110011 8,7,8,8,7,8,8,9,8,7,8,8,7,8,7,8,8,7,8,8,9,8,7,8,8,7,8,7,8,8,7,8,8,7,
%U A110011 8,7,8,8,7,8,8,9,8,7,8,8,7,8,7,8,8,7,8,8,7,8,7,8,8,7,8,8,9,8,7,8,8,7,8,7,8
%N A110011 a(n) = n-F(F(F(F(F(n))))) = n-F^5(n) where F(x)=A120613(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2.
%C A110011 To built the sequence start from the infinite Fibonacci word b(k)=floor(k/phi)-floor((k-1)/phi) for k>=2 giving 1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,..... Then replace each 0 by the block {9,8,7,8,8,7,8,7,8,8,7,8,8} and each 1 by the block {9,8,7,8,8,7,8,7,8,8,7,8,8,7,8,7,8,8,7,8,8}. Append the initial string {1,2,3,4,5,6,7,8,8,7,8,8,7,8,7,8,8,7,8,8}.
%D A110011 Benoit Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005.
%o A110011 (PARI) F(x)=floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*x)); a(n)=n-F(F(F(F(F(n)))))
%Y A110011 Cf. A005614 (infinite Fibonacci binary word), A120613.
%Y A110011 Cf. sequences for a(n) = n-F^k(n): A003842 (k=1), A110006 (k=2), A110007 (k=3), A110010 (k=4).
%K A110011 nonn,easy
%O A110011 1,2
%A A110011 _Benoit Cloitre_, Sep 02 2005