OFFSET
1,3
COMMENTS
The Ziv-Lempel encoding scans the sequence from left to right and inserts a comma when the current phrase (since the last comma) is distinct from all previous phrases (between commas).
It appears that a(n) is just the square of the period of the base 2 expansion of 1/n. For example, if n=3 the sequence of terms in the base-2 expansion of 1/3 is {0,1,0,1,0,1,0,1,...}, of period 2, whereas a(3)=4=2^2.
EXAMPLE
For n=3, the sequence of base-2 digits of 1/3 is {0,1,0,1,0,1,0,1,0,1,0,1,...}. The Ziv-Lempel encoding parses this into "phrases": {0}, {1}, {0,1}, {0,1,0}, {1,0}, {1,0,1}, {0,1,0,1}, {0,1,0,1,0}, {1,0,1,0}, {1,0,1,0,1}, {0,1,0,1,0,1}, ..., with lengths {1,1,2,3,2,3,4,5,4,5,6,7,6,7,8,9,8,9,10,11,...}. The differences are {0,1,1,-1,1,1,1,-1,1,1,1,-1,1,...} which quickly becomes periodic with period 4. Thus a(3)=4.
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Sep 24 2010
STATUS
approved