A132917 - OEIS

%I #17 Apr 29 2023 20:47:13

%S 233,89,178,34,267,123,212,68,157,13,246,102,191,47,280,136,225,81,

%T 170,26,259,115,204,60,293,149,5,238,94,183,39,272,128,217,73,162,18,

%U 251,107,196,52,285,141,230,86,175,31,264,120,209,65,298,154,10,243,99,188

%N 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 The sequence can also be built up from left to right directly (without having to make insertions) as follows:

%C a(0) equals greatest odd Fibonacci number less than n, i.e., [a(0) = F(2m)]

%C The rule for a(n+1) is according to the following (first listed takes priority):

%C a(n+1) = a(n) + F(2m) if less than or equal to n

%C a(n+1) = a(n) - F(2m-1) if greater than 0

%C a(n+1) = a(n) + F(2m-2)

%C Continue until all n terms have been included in the sequence.

%H Kenneth J Ramsey, Sep 05 2007, <a href="/A132917/b132917.txt">Table of n, a(n) for n = 0..299</a>

%F 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 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 Cf. A132828.

%K nonn,uned

%O 0,1

%A _Kenneth J Ramsey_, Sep 05 2007