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 A110006 #14 Sep 05 2024 08:10:19
%S A110006 1,2,3,3,2,3,3,4,3,2,3,3,2,3,3,4,3,2,3,3,4,3,2,3,3,2,3,3,4,3,2,3,3,2,
%T A110006 3,3,4,3,2,3,3,4,3,2,3,3,2,3,3,4,3,2,3,3,4,3,2,3,3,2,3,3,4,3,2,3,3,2,
%U A110006 3,3,4,3,2,3,3,4,3,2,3,3,2,3,3,4,3,2,3,3,2,3,3,4,3,2,3,3,4,3,2,3,3,2,3,3,4
%N A110006 a(n) = n-F(F(n)) where F(x)=A120613(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2.
%C A110006 To built the sequence start from the infinite Fibonacci word : b(n)=floor(n/phi)-floor((n-1)/phi) for n>=1 giving 0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,..... Then replace each 0 by the block {2,3,3} and each 1 by the block {2,3,3,4,3}. Append an initial 1.
%D A110006 Benoit Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005.
%o A110006 (PARI) a(n)=n-floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*n))))
%Y A110006 Cf. A005614 (infinite Fibonacci binary word), A120613.
%Y A110006 Cf. sequences for a(n) = n-F^k(n): A003842 (k=1), A110007 (k=3), A110010 (k=4), A110011 (k=5).
%K A110006 nonn,easy
%O A110006 1,2
%A A110006 _Benoit Cloitre_, Sep 02 2005