OFFSET
1,2
COMMENTS
I have found two patterns for this sequence. The first is that there is a pattern 0,3,6,0,3,6,0,3,6,... which states the lengths of the "LessThanList" for each term. In other words, a(6) = 12. There are six integers less than 12 which are not already listed in the sequence at this point, {3,4,6,8,10,11}. a(7) = 3. There are no integers not already on the list which are less than 3 at this point. a(8) = 10. There are three integers less than 10 which are not already on the list at this point, {4,6,8}. Also, after the 14th term, the sequence becomes regular in the following way. The difference between successive terms is as follows: 5,-13,11,5,-13,11,... . - Diana L. Mecum, Aug 15 2008
LINKS
Diana Mecum, Table of n, a(n) for n = 1..1011 [From Diana L. Mecum, Aug 15 2008]
EXAMPLE
The first 5 terms of the sequence can be plotted on the number line as:
1,2,*,*,5,*,7,*,9,*,*,*.
Now a(5) is 7. Counting down from 7 gets a noncomposite (1,2, or 3) number of steps to arrive at each yet unused positive integer. So we instead count up 4 positions, skipping the 9 as we count, to arrive at 12 (which is at the rightmost * of the number line above).
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Nov 17 2005
EXTENSIONS
Terms a(14) through a(1011) from Diana L. Mecum, Aug 15 2008
STATUS
approved