OFFSET

1,2

COMMENTS

The sequence A138007 is defined using this sequence, in the same way as A138007 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 A138007(2)=2nd term:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ...

Remove every A138007(3)=4th term:

1, 3, 5, 9, 11, 13, 17, 19, ...

Remove every A138008(4)=5th term:

1, 3, 5, 9, 13, 17, 19, ...

and so on.

CROSSREFS

KEYWORD

nonn

AUTHOR

Sune Kristian Jakobsen (sunejakobsen(AT)hotmail.com), Feb 27 2008

STATUS

approved