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Search: id:A138008
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| A138008 |
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Produced by a sieve: Start with the natural numbers; at the k'te step remove every A138007(k+1)-th term of the sequence remaining after the (k-1)-st sieving step. |
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2
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| 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
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OFFSET
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1,2
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COMMENT
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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
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EXAMPLE
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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.
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CROSSREFS
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Cf. A138007.
Sequence in context: A018533 A076052 A050556 this_sequence A063954 A123509 A063915
Adjacent sequences: A138005 A138006 A138007 this_sequence A138009 A138010 A138011
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KEYWORD
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nonn
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AUTHOR
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Sune Kristian Jakobsen (sunejakobsen(AT)hotmail.com), Feb 27 2008
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