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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.
2
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.
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
KEYWORD
nonn
AUTHOR
Sune Kristian Jakobsen (sunejakobsen(AT)hotmail.com), Feb 27 2008
STATUS
approved