OFFSET
1,2
COMMENTS
a(n) - a(n-1) is in {1,2,3} for n>=2, and a(n)/n -> 2. These are also the positions of 1 in the {0->10, 1->01}-transform of the Pell word, A171588.
From Michel Dekking, Sep 19 2019: (Start)
Here is a precise description of the sequence of first differences.
Let tau be the map tau: 0->01, 1->10. By definition A286685 equals tau(b), where b is the Pell word. The words of length 2 occurring in b are 00, 01 and 10. These are mapped by tau to
tau(00) = 0101, tau(01) = 0110, tau(10) = 1001.
Each of these three four letter words contains exactly 2 0's, occurring among the first two letters and among the last two letters. It follows from this that the overlapping words of length 2 in the Pell word b induce distances between 0's in tau(b) of 2 for 00, of 3 for 01, and of 1 for 10. But then the difference sequence (a(n+1) - a(n)) = 2, 3, 1, 2, 3, 1, 2, ... is equal to the 1->3, 2->1, 3->2 permuted version of the 3-symbol Pell word A294180. (End)
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
As a word, A286685 = 01011001011001010110010110..., in which 0 is in positions 1,3,6,7,9,12,...
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 13 2017
STATUS
approved