OFFSET
1,2
COMMENTS
The sequence A138008 is defined using this sequence, in the same way as A138008 is used to define this sequence.
The sequences can be found this way:
Define a(n,1)=n.
Now write the natural numbers and run this sieve: In the k-th step remove every a(k+1,1)-th number that remained after k-1 step. You will get this:
1, 3, 7, 13, 19, ... (A000960).
Now let a(n,2) be n-th number in this sequence.
In the same way: Define a(n,i+1) to be the n-th number left after running the similar sieve on the natural numbers using a(n,i) instead of a(n,1). Now:
a(n,2i+1)-> A138007(n) when i->infinity and,
a(n,2i)-> A138008(n) when i->infinity.
EXAMPLE
Start with the natural numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...
Remove every A138008(2)=3rd term:
1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, ...
Remove every A138008(3)=5th term:
1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20, ...
Remove every A138008(4)=9th term:
1, 2, 4, 5, 8, 10, 11, 13, 17, 19, 20, ...
and so on.
CROSSREFS
KEYWORD
nonn
AUTHOR
Sune Kristian Jakobsen (sunejakobsen(AT)hotmail.com), Feb 27 2008
STATUS
approved