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

1, 2, 4, 5, 8, 10, 11, 13, 17, 19, 20, 23, 26, 28, 31, 34, 38, 40, 43, 46, 47, 50, 55, 56, 58, 61, 64, 68, 71, 76, 77, 80, 85, 86, 92, 94, 95, 98, 101, 103, 106, 109, 115, 118, 122, 124, 125, 128, 137

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.

Links

Table of n, a(n) for n=1..49.

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

Cf. A138008.

Sequence in context: A185392 A324700 A191987 * A284880 A047261 A286687

Adjacent sequences: A138004 A138005 A138006 * A138008 A138009 A138010

Keyword

nonn

Author

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

Status

approved