A138008 Produced by a sieve: Start with the natural numbers; at the k-th step remove every A138007(k+1)-th term of the sequence remaining after the (k-1)-st sieving step.

1, 3, 5, 9, 13, 17, 19, 27, 29, 35, 43, 45, 57, 59, 61, 67, 81, 83, 93, 99, 107, 115, 123, 125, 137, 141, 149, 163, 165, 173, 189, 195, 201, 213, 217, 219, 229, 243, 249, 267, 269, 275, 283, 297, 307, 313

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.

Links

Table of n, a(n) for n=1..46.

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

Cf. A138007.

Sequence in context: A076052 A340377 A050556 * A063954 A123509 A196094

Adjacent sequences: A138005 A138006 A138007 * A138009 A138010 A138011

Keyword

nonn

Author

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

Status

approved