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Search: id:A138007
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| A138007 |
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Produced by a sieve: Start with the natural numbers; at the k'te step remove every A138008(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, 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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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 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.
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CROSSREFS
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Cf. A138008.
Sequence in context: A161790 A131396 A131391 this_sequence A047261 A102798 A004612
Adjacent sequences: A138004 A138005 A138006 this_sequence A138008 A138009 A138010
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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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