cp's OEIS Frontend

A132917 Order set of the first 300 infinite truncated Fibonacci Words where a(n) is the number of terms (ones and zeros) truncated from the left hand side of the word.

%I A132917 #17 Apr 29 2023 20:47:13
%S A132917 233,89,178,34,267,123,212,68,157,13,246,102,191,47,280,136,225,81,
%T A132917 170,26,259,115,204,60,293,149,5,238,94,183,39,272,128,217,73,162,18,
%U A132917 251,107,196,52,285,141,230,86,175,31,264,120,209,65,298,154,10,243,99,188
%N A132917 Order set of the first 300 infinite truncated Fibonacci Words where a(n) is the number of terms (ones and zeros) truncated from the left hand side of the word.
%C A132917 The sequence can also be built up from left to right directly (without having to make insertions) as follows:
%C A132917 a(0) equals greatest odd Fibonacci number less than n, i.e., [a(0) = F(2m)]
%C A132917 The rule for a(n+1) is according to the following (first listed takes priority):
%C A132917 a(n+1) = a(n) + F(2m) if less than or equal to n
%C A132917 a(n+1) = a(n) - F(2m-1) if greater than 0
%C A132917 a(n+1) = a(n) + F(2m-2)
%C A132917 Continue until all n terms have been included in the sequence.
%H A132917 Kenneth J Ramsey, Sep 05 2007, <a href="/A132917/b132917.txt">Table of n, a(n) for n = 0..299</a>
%F A132917 The sequence is generated starting with {2,1} and the numbers 3,4,5,..n are inserted in order into the sequence using the following rules: If n is an even Fibonacci number, it is inserted after the last term If n is an odd Fibonacci number, it is inserted before the first term If n is not a Fibonacci number, it is inserted between the adjacent terms, n - GF(even) and n-GF(odd) where GF(odd) and GF(even) are respectively the greatest odd and even Fibonacci numbers less than n.
%e A132917 4 appears between 2 and 1 in the sequence because the greatest odd Fibonacci number less than 4 is 2 and the greatest even Fibonacci number less than 4 is 3
%Y A132917 Cf. A132828.
%K A132917 nonn,uned
%O A132917 0,1
%A A132917 _Kenneth J Ramsey_, Sep 05 2007